COURSE DESCRIPTIONS
Language and Logic Courses
Advanced Courses
Thomas Stephen and Fausto Carcassi
This course introduces students to the formal tools and theoretical background to be able to formulate and address questions about universals of the composition function in natural language. A satisfactory evolutionary account of compositionality has to explain not just compositionality as such, but the specific set of observed operations or some tightly fitting empirical constraints on the observed variation in the composition operator, as in the successful tradition of Generalized Quantification Theory. Empirical observations have motivated a rich inventory of modes of composition, including function application, type shifting, predicate modification, and less widely accepted or theory-specific ones such as event identification, restriction, and intensional variants of each. Despite the wealth of empirical data and a few scattered attempts to address the issue, to date there has been little interest in formulating and explaining universals of natural language composition. In this course, we aim to address these topics directly by surveying the empirical landscape, describing the composition function as a single operation on meanings, introducing some richer type theories to formalize this operation, and formulating some universals that constrain the observed variation. Students will gain practice with these tools and explore how they can be applied to formulate hypotheses about universals of semantic composition.
Advanced Topics in Logical Geometry
Lorenz Demey and Stef Frijters
Aristotelian diagrams, such as the square of opposition, provide a fundamental perspective on the intricate interplay between relations of implication (entailment) and opposition (negation). These diagrams have a rich history in philosophical logic, and today they are also widely used in disciplines such as linguistics and computer science. Over the past two decades, Aristotelian diagrams have begun to be studied as objects of independent interest, giving rise to the burgeoning field of logical geometry. This course will deal with advanced topics in logical geometry, such as (i) the category-theoretical foundations of the classification of Aristotelian diagrams, (ii) the interaction between bitstring semantics and logic-sensitivity, (iii) generalizing Aristotelian diagrams beyond binary relations, (iv) the modal logic of Aristotelian diagrams (i.e., viewing these diagrams as Kripke models), and (v) a diagrammatic reasoning system for Aristotelian diagrams. Despite the advanced nature of this course, no specific prior knowledge regarding Aristotelian diagrams is required, as we will start the course by introducing all the basic tools and insights from logical geometry.
Norm-Sensitivity Beyond Gradable Expressions
Linmin Zhang and Yael Greenberg
"Mary is tall" means that her height exceeds a contextual norm. In formal semantics, such uses of gradable adjectives (e.g., "tall") are considered the prototypical case of norm-sensitivity. However, beyond gradable expressions, norm-sensitivity has also been observed to arise with focus particles like "even" and "only", exclamatives like "what a day", and their cross-linguistic counterparts. Related phenomena are sometimes discussed using terms like mirativity and evaluativity. This course surveys and critically examines recent research on the norm-sensitivity of such non-gradable constructions. We begin with an introduction to gradability and norm-sensitivity. The course then focuses on norm sensitivity in the family of "only"-like and "even"-like particles, exploring the division of labor between lexical meaning and pragmatic inference. We also consider how analyses of "only"-like and "even"-like particles (i) extend to other phenomena, such as wh-exclamatives and concessives, and (ii) shed new light on the norm-sensitivity of gradable expressions.
Team Semantics: Linguistic and Philosophical Applications
Aleksi Anttila and Marco Degano
This course introduces team semantics, with a focus on linguistic and philosophical applications. In team semantics formulas are evaluated with respect to sets of assignments, or "teams", rather than single assignments, as in "classical" semantics. Team semantics provides powerful tools for modeling phenomena relevant to formal semantics and philosophical notions. Students will explore its linguistic applications, including the analysis of free choice and disjunction, questions, indefinites, and plurality. Philosophical perspectives will address connections to truth, negation, and modality. The course combines technical development of the logical frameworks with critical examination of their conceptual significance. By the end, participants will gain a solid foundation in team semantics and its applications, equipping them with the knowledge and tools to engage in current debates at the intersection of logic, language, and philosophy.
Type-Lowering and Paradox in Natural Language
Øystein Linnebo and Eric Snyder
Certain semantic phenomena in natural language raise foundational challenges for semantic theory because their most obvious analyses threaten to introduce paradoxes, e.g. Russell’s. Traditionally, such phenomena include at least group-formation (‘Some students gathered’ → ‘A group of students gathered’) and nominalization (‘Too much fun is not fun’); they may also include kind-reference and constructions like ‘the color red’. The purpose of the course is to provide a systematic introduction to the range of such phenomena, highlighting the threat of paradox that each gives rise to. We will also discuss some proposed responses to these threats, specifically by appealing to notions such as potentiality and constructability.
Introductory Courses
Marco Degano and Robert van Rooij
Vagueness is a pervasive feature of natural language: terms like heap, tall, or bald admit borderline cases and generate paradoxes such as the Sorites. This course introduces students to the central logical and philosophical responses to vagueness, while providing a broader training in non-classical logics. We will survey many-valued logics, supervaluationist approaches, epistemicism, contextualist accounts, and modern approaches like strict-tolerant logics. Each framework will be developed formally and assessed against key desiderata, such as preserving classical reasoning, addressing the Sorites paradox, and capturing linguistic usage. The course thus serves three overlapping audiences: philosophers interested in the conceptual foundations of vagueness; logicians concerned with the design and application of non-classical logics; and linguists studying the semantics of vague expressions. Using vagueness as a case study, participants gain both a technical toolkit and a critical perspective on how logical systems can be built and applied to model philosophically significant phenomena.
On the plurality of the verbs: Attitudes of knowledge and belief
Natasha Korotkova
Website: https://natasha-korotkova.github.io/teaching/ESSLLI2026/
Propositional attitude reports — expressed by predicates like “believe”, “intend”, “know”, “want” — are a foundational topic in linguistics and philosophy of language. Research on attitudes sits at the intersection of several areas: the syntax of clausal complementation, the semantics of intensional environments, the nature of meaning, the structure of mental representations. Recently, there has been an explosion of cross-linguistic work on the fine-grained semantics of attitude predicates. However, this fruitful research agenda is largely disconnected from the work on attitudes within philosophy of mind and psychology. To what extent does the linguistic behavior of attitude predicates reflect the underlying differences in attitudes they describe? This course addresses this central question through a multi-faceted guided tour of doxastic predicates beyond ‘know’ and ‘think’. Taking inspiration in classical lexical semantics, it examines natural classes found within those predicates, with special attention to their cognitive underpinnings and to the core concepts ‘knowledge’ and ‘belief’.
Introduction to the semantics and pragmatics of anaphora
Keny Chatain and Benjamin Spector
Pronouns such as “she”, “it”, etc, are an integral part of what allows language to express complex and cohesive thoughts efficiently, and to create anaphoric links within sentences and across sentences. Arguably, pronouns or pronominal elements are pervasive in the lexicon and across languages. They are one of language’s preferred tools to introduce a dependency on ‘context’. But what is context? How does the meaning of sentences depend on context? By studying pronouns and anaphora, semanticists have gained a unique perspective into these general questions. For good reason, pronominal anaphora have frequently motivated radical departures from standard assumptions about the interplay of contextual information and sentence meaning (e.g., dynamic semantics).
The goal of this class is to familiarize students with the critical data (e.g. donkey sentences, bathroom sentences, existential/universal readings), both theoretical and empirical, around which debates revolve, and provide a gentle introduction to both leading and recent theories seeking to explain these facts, including dynamic semantics and recent static proposals. We will also explore the broader consequences of these theories for the architecture of a theory of meaning.
Larry Moss
This is a course on logic done in fragments of natural language. We are interested in inference rather than semantics, and we use 'small' logics rather than via translation to any standard logical system. The course is an updated version of an ESSLLI course from 2010, and to more recent versions of the course held at NASSLLI and similar venues. But I have updated it in several ways, including by discussing monotonicity in natural language and also inference on large language models. The first two days presents a set of logical systems that are extended syllogistic logics. Since the course has a lot of completeness theorems, it will have a high technical content. Then the course looks at monotonicity. Finally, it discusses the NLI field and how logic and language models can work together, and what the challenges are in doing so. It uses computer tools of various sorts.
Conditionals in Decision Theory
Calum McNamara and Paolo Santorio
Many decision theories make essential use of conditionals in defining expected utilities. Indeed, on some proposals (e.g. Lewis 1981, Joyce 1999), the difference between various kinds of decision theory can all be captured via differences in the meaning of the conditional operator used to define expected utility. This tight connection between decision theory and conditionals is theoretically fruitful, but it also raises problems. For instance, Gibbard (1981) showed that under plausible assumptions, attempts to define rational choice in terms of subjunctive conditionals lead to a “collapse” result, blurring the distinction between evidential and causal decision rules. Likewise, Lewis (1981) and Joyce (1999) claim that the version of causal decision theory mentioned above is equivalent to various other versions. But if that’s so, then it’s possible to generate a “triviality result” for causal decision theory, in the style of Lewis (1976).
This course will examine the interface between decision theory and conditionals, and how this may help solve open problems in decision theory. Topics will include: the implications for decision theory of building causal structure into the semantics of counterfactuals; debates about which kind of conditional is relevant for decision-making (either indicatives or subjunctives); the relationship between Lewisian triviality results and decision theory; the use of conditionals in “dynamic” decision problems; and so-called “logical counterfactuals”, as employed in more recent versions of decision theory, like “functional decision theory”.
Dean McHugh
This course provides an introduction to an old but neglected analysis of modality, called 'Conditional modality'. The analysis was originally developed for deontic modality (what is obligatory, permitted, should happen, and so on) in the 1950s by Alan Ross Anderson, Stig Kanger, and Risto Hilpinen, preceding the later development of Kripke semantics and Kratzer's work on modality. Since then, however, the analysis has largely been forgotten in contemporary work on modality.
The central idea is that something is obligatory just in case if it does not happen, the rules have been broken, while something is permitted just in case if it does happen, the rules have not been broken. Thus the analysis puts conditionals at the core of modal concepts. As we will see, this analysis can be generalised to all modal flavours, such as epistemic modals.
A central focus of the course is to compare conditional approaches to modality with the standard treatment, such as Kripke semantics and Angelika Kratzer's work. Among the phenomena we cover are failures of Inheritance (the principle that necessity and possibility are closed under logical consequence), free choice (the failure of the inference from 'Possible A' to 'Possible(A or B)'), and the role of context dependence in modal statements.
The course provides a friendly introduction to standard treatments of modality in formal semantics. At the same time, it goes beyond standard treatments of the topic by bringing conditional modality to the fore. The course will be accessible to students with no formal background.
Probability logic, language, and cognition
Niki Pfeifer
Uncertainty is ubiquitous in everyday life communication and reasoning. In this course, we will learn about methods and tools to understand language and cognition under uncertainty. We will get interdisciplinary perspectives by combining formal-philosophical and experimental-psychological approaches. In particular, we will understand why Coherence-based Probability Logic offers a unified rationality framework for studying diverse phenomena including conditionals, counterfactuals, connexivity, quantification, reasoning, and argumentation on the normative level. Moreover, on the descriptive level, we will become familiar with recent experimental-psychological results on linguistic phenomena, cognition, and reasoning under uncertainty. Specifically, we will learn about formal and experimental work on nonmonotonic reasoning, conditionals, counterfactuals, quantification, and argumentation. Finally, we will achieve a deeper understanding of what it means to be rational under incomplete knowledge and uncertainty.
Jéssica Mendes and Jonathan Caleb Kendrick
The apparent failure of Antecedent Strengthening is often seen an argument for nonmonotonic theories of conditionals. At the same time, the licensing of Negative Polarity Items (NPIs) in conditional antecedents seems to call for a downward-monotone semantics. In this course, we present some of the classic work developed to dissolve this tension and reassess it in the light of modern developments in polarity sensitivity and in the semantics of conditionals. In doing so, we provide students with in-depth understanding of prominent theories of conditionals and polarity sensitivity, and bring their attention to important open questions in this area.
Attitude adjustment: Trends in the semantics of clausal-embedding
Deniz Ozyıldız and Tom Roberts
This course will provide an introduction to the semantics of attitude predicates like believe, know, and want. We will focus in particular on two major influential treatments of attitudes: as modal operators (Hintikka 1962, 1969, et seq.) or as predicates of eventualities, with modality being contributed by, e.g., complementizers (Kratzer 2006; Moulton 2009, 2015; Elliott 2019). We will
examine how these competing accounts handle a range of empirical phenomena, including de re/de dicto readings, the ability of some predicates to combine with both declarative and interrogative clauses, and the encoding of inferences like factivity and neg-raising. We will conclude by examining some open issues in the semantics of attitudes, including whether the grammar renders certain plausible attitude meanings ‘impossible’ to lexicalize (e.g., the idea that there are no contra-factive predicates), the role of lexical aspect in clause embedding, and how data from understudied languages has challenged old generalizations.
Experimental and theoretical investigations of affect in language and cognition
Michelle Stankovic and Morgan Moyer
Affect is fundamental to how humans think and communicate, yet its role in language and cognition has often been overlooked. This course offers a focused introduction to the experimental and theoretical study of affect, combining contemporary perspectives from linguistics, psychology, and philosophy. Students will be introduced to core experimental methods of affect used across both the linguistics and psychology disciplines as part of an exploration of research methodology (e.g., reaction time tasks, implicit measures including priming, lexical decision paradigms, acceptability tasks, corpus analyses, and a brief discussion of neuroimaging), with attention given both to design elements (e.g., materials, power) and analysis (e.g., models, practical execution). The course includes a practical component, where students will apply the knowledge through a (mini) study replication, involving data collection, analysis, and visualisation. The toolkits for this practicum include PCIbex, R Studio. This course will help students design, execute and evaluate experiments involving affective variables.
Foundational Courses
The lambda calculus and simple type theory: A toolkit
Howard Gregory
Since the work of Richard Montague (d. 1971), the typed lambda calculus has been the representation language of choice for research in logical linguistics. This course offers linguists a foundation in lambda notation and the derivation of compositional meanings through types. We then study natural deduction and the `constructive' tracking or labelling of logical proofs. The centre of the course, as of much research, is the Curry-Howard correspondence between the two approaches, which will be set out in some detail. Finally we explore its use in modern linguistics, including some extensions of the basic correspondence. The course includes intuitive examples of the use of these techniques both in classical Montague-style semantics and contemporary research.
Language and Computation Courses
Advanced Courses
Vector representations of morphological processes
Rossella Varvara
Website: https://sites.google.com/view/rossellavarvara/teaching/ESSLLI2026
Word embeddings (also known as distributional semantic models or vector space models) have been proved as an invaluable tool in natural language processing for modeling word meaning. Beyond their success in NLP, these models are increasingly used in theoretical linguistics for their potential to support large-scale, quantitative investigations of semantic phenomena (Lenci 2018; Boleda 2020; Wauquier 2022 for reviews).
In this course, we will explore the application of DSMs to the study of the semantics of morphological processes. We will address a range of distributional measures that can be used to assess semantic properties of affixes, including transparency, affix similarity and competition, morphological regularity, polysemy of derived forms, and affix polyfunctionality. Through selected case studies, it will be shown how these computational methods contribute to our theoretical understanding of morphological processes. The course will be hands-on: students will learn how to derive morphological representations and how to compute different measures in python.
The Logic Underlying Language Models
Ryan Cotterell
Language models built on architectures such as recurrent neural networks (RNNs), transformers, and state-space models (SSMs) have achieved remarkable success in natural language processing (NLP). To better understand their expressivity and limitations, researchers have increasingly turned to theoretical analyses grounded in formal methods. Recent work has characterized these models through diverse frameworks, including formal languages, circuit complexity, logical, and programming languages. The growing diversity of both architectures and analytical approaches has created fragmentation in the field, making it challenging for newcomers to navigate and synthesize existing results. This course aims to bridge these gaps by providing a unified and accessible overview of formal methods used to characterize language models. It highlights how these theoretical perspectives—ranging from automata theory to circuit complexity—can be systematically interpreted within the framework of formal logic. By grounding these analyses in a single, intuitive logical perspective, this course seeks to make the theoretical understanding of language model expressivity more coherent and approachable to a broader audience.
Computational Models of Conversational Grounding
David Traum and Kristiina Jokinen
Conversational Grounding is the process by which participants in a conversation establish new common ground. This process includes not just transmission of declarative utterances, but inferential and feedback processes. This process is also of critical importance to artificial dialogue systems, which include additional challenges of imperfect input recognition, and limited ontologies and inferential ability. In this course we will review models and uses for common ground in pragmatics and computational agent theories, and then examine a variety of proposals of how common ground can be established. These proposals include both descriptive analyses of behavior, as well as generative proposals that can be used by computational systems engaged in dialogue to decide on next moves. We will also look at multimodal grounding, and advanced topics, including multiparty grounding, incremental grounding and degrees of grounding, as well as how grounding models have been used for studying other social phenomena. We will also look at how current AI Large Language Models (LLMs) engage in conversational grounding differently from people and how LLMs can be used to monitor conversational grounding.
Advanced Course for Language and Computation Area (this will be an updated version of an ESSLLI course last taught in 2022).
Introductory Courses
The laws of probabilistic phonology
Giorgio Magri
This course focuses on token or inherent variation in phonology. The main goal is to collect to- gether and systematize a number of substantive and more formal empirical generalizations on rates of application of variable phonological processes that have been formulated in the older variationist literature, in the more recent constraint-based phonological literature, as well as in the psycholinguis- tic literature. The intention is that these generalizations should provide the basis for mathematical analysis to characterize the grammatical frameworks that are compatible with them. The course will be based on an extended version of Magri and Flemming (2025), available here. These materials will be turned into detailed lecture notes for the course.
Foundational Courses
Introduction to Opinion Mining and Social Media Language Analysis
Omnia Zayed
Public opinion, speculation, and (mis)information have a profound impact on our lives in many ways. It affects democratic decisions, policymaking, and emergency reactions. The unprecedented amount of data available online creates a pressing need for automated language analysis to understand public discourse and visualise patterns/relationships through statistical analysis and results aggregation. In this course, we will introduce opinion mining and provide a comprehensive understanding of natural language processing techniques involved in analysing opinionated text on multiple levels. The course will cover the essential concepts of identifying a wide range of opinion dimensions, including sentiment, emotions, aspects, suggestions, figurative language, hate speech, misinformation, propaganda, and conspiracy, expressed in various textual data sources. Students will also gain hands-on experience with state-of-the-art approaches and algorithms used in this area in a real-world application. We conclude by discussing the potential benefits of utilising these tasks for analysing social media language, touching on their role in facilitating two-way communication during social crises as well as their societal impact and ethical implications. This course builds on the success of the one introduced in ESSLLI 2025, which gained the attention of students from various fields.
From Speech Act Theory to Dialogue Act Modeling
Maryam Mohammadi and Hendrik Buschmeier
In this course, we will trace the development from speech act theory to dialogue act modeling, bridging the fields of philosophy, linguistics, and computational linguistics. We will introduce foundational linguistic approaches (from Austin’s traditional theory to more conversational based frameworks) and examine how these perspectives have influenced dialogue analysis and modeling in computational linguistics. The course will also explore selected implemented models, assessing their performance. Finally, we will outline how large language models (LLMs) behave and handle (indirect and complex) speech acts.
Logic and Computation Courses
Advanced Courses
Verifying graph neural networks
François Schwarzentruber
This advanced course is about verifying graph neural networks. We will survey the main results about the expressivity of graph neural networks. We will discuss a methodology to verify the behaviors of GNNs, present their link with counting logics, and describe verification algorithms.
Thomas Meyer and Ivan Varzinczak
This course aims at providing an introduction to reasoning defeasibly over description logic ontologies in the context of knowledge representation and reasoning in AI. Description Logics (DLs) are a family of logic-based knowledge representation formalisms with appealing computational properties and a variety of applications. The different DLs proposed in the literature provide a wide choice of constructors in the object language. However, these are intended to represent only classical, monotonic knowledge, and are therefore unable to express the different aspects of uncertainty and vagueness that often show up in everyday life, such as typicality and exceptions. A similar criticism can be made against the use of classical DLs at the level of entailment, i.e., that of reasoning from a knowledge base: in many practical applications we need notions of consequence that are more powerful and robust than the standard Tarskian one.
The goal of this course is two-fold: (i) to provide an overview of the development of non-monotonic approaches to DLs from the past 25 years, pointing out the difficulties that arise when naively transposing the traditional propositional approaches to the DL case, and (ii) present the latest results in the area and technical questions that remain open for investigation.
Reasoning in graph games: A modal logic study
Sujata Ghosh and Dazhu Li
There is a long tradition of interaction between logic and games. In the past two decades, games played on graphs have proven to be a concise model for a wide range of interactive scenarios, including adverse circumstances with blocking/sabotaging your opponents in achieving their goals, and beneficial situations of learning through modifying the choice of methodologies. Pursuit-evasion environments provide further scenarios towards search problems and similar others. These games have deep roots in the study of many areas, e.g., graph theory and algorithms, abstract argumentation theory, computational complexity among others.
These graph games have quite attractive analogies with respect to modal logic semantics and have motivated many new designs of logical systems that can capture crucial structures of these games. An important aspect is to define the desired logical tools to characterize key features of the games, including actions of the players, their winning strategies, and also, informational updates regarding players’ uncertainties in the game plays. In recent years, many efforts have been made to explore the interactions between the two areas, but significant challenges remain.
This advanced course is proposed to introduce the ESSLLI 2026 participants to the basic ideas and recent developments in this area, and also to the open questions that still remain. It is advanced in the sense of requiring conceptual maturity while remaining technically elementary.
Gaia Belardinelli and Snow Zhang
We are unaware of many things, and unaware that we are unaware of them. But what is (un)awareness, and how does it relate to other epistemic notions such as belief, knowledge and uncertainty? In this course, we will introduce models of awareness that have been developed in philosophy, computer science and economics. The topics that we will discuss include: the problem of logical omniscience, the Dekel-Lipman-Rustichini impossibility result, syntactic vs. semantic models of awareness and their respective sound and complete axiomatizations, awareness dynamics, (un)awareness and decision theory and reverse Bayesianism.
Anupam Das
'Non-wellfounded' and 'cyclic' proofs have emerged in the last 30 years as a powerful mechanism to reason about systems with (co)induction. They are an alternative to usual well-founded proofs with (co)induction principles, that are seemingly more powerful at the level of expressivity, and more intuitive at the level of proof search, often avoiding elusive invariants.
In this course we shall introduce students to the foundations of cyclic proof systems. We shall present the core theory, based on seminal results in the literature. Moreover we shall give the students the tools they need to apply these techniques to new logics and theories.
Introductory Courses
Tableaux-based decision methods for modal, temporal, and epistemic logics
Valentin Goranko and Dmitry Shkatov
This course will develop systematically and illustrate with examples the tableaux-based methodology for constructive testing of satisfiability and model building, applicable to a wide variety of logical systems. It will be first illustrated on standard propositional modal logics, then on linear and branching time temporal logics, and then on multi-agent epistemic logics involving individual, common, and distributed knowledge.
We will sketch proofs of termination, soundness, and completeness of the tableau methods and will show how satisfying models can be extracted from open tableaux.
The main objectives of the course are to give the students some practical skills of applying the methods presented in the course and the theoretical understanding of the underlying tableau-building methodology that would enable them to construct similar decision methods for other logics of their interest.
The course will be accessible and appealing to a broad audience of students and researchers in philosophy, mathematics, computer science, and AI.
Algebraic Automata Theory: A Rosetta Stone for Computer Scientists
Nicola Gigante
Algebraic Automata Theory studies automata, and their accepted languages, through the algebraic theory of semigroups, monoids, and groups. The field has a long history dating back to the work of Schützenberger, starting in the '50s of last century, and became popular thanks to his seminal result linking star-free languages and aperiodic monoids. Unfortunately, most computer science curricula in the last decades diverged from the mathematical prerequisites needed to fully grasp algebraic automata theory, namely group theory and the theory of semigroups. As a consequence, the field can be most of the time hard to approach. In this course, we provide an introduction to algebraic automata theory meant for the computer science researcher who is already proficient in automata theory but never received formal training on abstract algebra in general and group and semigroup theory in particular. We start from the very basics up to a self-contained proof of Schützenberger's theorem.
Combinatorial Games in Finite Model Theory
Phokion Kolaitis
The study of the expressive power of logics is a main strand of finite model theory. Combinatorial games, played between two players, called the Spoiler and the Duplicator, provide a sound and complete methodology for analyzing the expressive power of first-order logic, as well as certain extensions of first-order logic, on classes of finite structures. The aim of this course is to introduce four different families of games, namely, Ehrenfeucht-Fraisse games, pebble games, bijection games, and multi-structural games, to establish the main results linking these four games to logical resources, and to illustrate their uses in analyzing the expressive power of logics in the finite. The course will also include a survey of results concerning the computational complexity of determining the winner of a given instance of one of these combinatorial games.
Logical Bilateralism - Proofs, Models and Applications
Sara Ayhan and Greg Restall
Logical bilateralism is an approach to meaning and consequence that foregrounds a symmetry between certain notions, like assertion and denial, proof and refutation or truth and falsity. Bilateralist approaches to such dual distinctions take both sides as primitive rather than—as in conventional 'unilateralist' approaches—taking one notion to be fundamental and defining the other in its terms. In recent years different bilateralist logical systems have been developed, displaying a wide variety in their specific orientation. What is missing so far is a systematic framework putting these very different approaches on a map and thereby highlighting similarities, distinctions and connections between them. Though giving a complete picture will also not be possible within the scope of the intended course, our aim is to familiarize the attendants with many different forms of logical bilateralism and use these to exemplify both the variety of approaches and the coherence of the underlying principles.
Logics of dependence and independence
Fan Yang
This course provides a concise introduction to logics of dependence and independence (DIL), which are formalisms for reasoning about dependence and independence relations in sciences. We will study the novel semantics of DIL--team semantics. The basic idea of team semantics is that dependency properties can only manifest themselves in multitudes, and thus formulas of DIL are evaluated on sets of assignments (called teams) instead of single assignments as in the usual Tarskian semantics. A team can be naturally viewed as a database, a dataset, an information state, etc. Thanks to the simple structure of teams and the abundance of their interpretations in various fields of science, DIL have found a number of applications in addressing issues in database theory, social choice, quantum theory, formal linguistics, and so on.
This introductory course will cover the fundamentals of team semantics and the core theory of first-order and propositional DIL.
Formal Verification of Multi-Agent Systems. Why, What, and Especially: How?
Catalin Dima and Wojciech Jamroga
Automated verification of discrete-state systems has been a hot topic in computer science for over 40 years. The idea found its way into AI and multi-agent systems in late 1990’s, and techniques for verification of such systems have been in constant development since then. Model checking of temporal, epistemic, and strategic properties is one of the most prominent and most successful approaches here. In this course, we present a brief introduction to the topic, and mention relevant properties that one might like to verify this way. Then, we describe some recent results on incomplete model checking algorithms and model reductions, which can potentially lead to practical solutions for the notoriously hard problem. On the way, we also present some experimental tools which can be used specify and verify multi-agent systems.
Proofs without syntax: An introduction to proof nets and combinatorial proofs
Willem Heijltjes and Lutz Straßburger
Introductory course on graphical proof representations.
A Gentle Introduction to Description Logics
Ivan Varzinczak
This course provides a gentle introduction to Description Logics (DLs) and their usefulness in knowledge representation and reasoning. DLs are a family of logic-based formalisms with interesting computational properties and a variety of applications. Most importantly, DLs are well-suited for representing and reasoning about terminological knowledge and constitute the formal foundations of semantic-web ontologies and, in particular, the W3C Web Ontology Language. There are different flavours of DLs with specific expressive power and applications, such as ALC, and on which we shall have a strong focus in this course. We start with a motivation for representing and reasoning with ontologies. We then present the description logic ALC, its syntax, semantics, logical properties, and proof methods, with a focus on the tableau-based one. Finally, we illustrate the usefulness of DLs with the popular Protégé ontology editor, a tool allowing for both the design of DL-based ontologies and the ability to perform reasoning tasks over them.
Stone Duality: Connecting Algebra and Topology via Logic
Levin Hornischer
This course is an introduction to Stone duality, which is an exciting area of logic and neighboring disciplines like math, computer science, and philosophy. Stone's theorem says that certain algebras (Boolean algebras) are in a precise sense equivalent to certain topological spaces (zero-dimensional compact Hausdorff spaces). The underlying idea is that the two seemingly different perspectives—the algebraic one and the spatial one—are really two sides of the same coin:
- formulas of a logic vs. its models,
- open sets of a space vs. its points,
- observable properties of a computational process vs. its denotation
- propositions vs. possible worlds.
After an interdisciplinary motivation, the course will introduce the mathematical theory, followed by applications. The goal is to show both the conceptual and technical potential of dualities by translating between the two sides and thus using their respective advantages.
Pavel Naumov
Website: https://pavelnaumov.com/esslli-26
Collective decision-making processes have a common pitfall: when things go awry, it is usually hard to identify a singleperson who should be blamed for the harmful outcome of a collective decision. Could collective decision-making processes be designed to avoid this? This question is at the core of responsible mechanism design — a new interdisciplinary area of research on the border of philosophy, game theory, logic, and artificial intelligence to be introduced in this course. We will discuss multiple formal definitions of responsibility and individual accountability, study whether the individual accountability requirement is consistent with shared authority, and cover design techniques for enforcing various forms of individual accountability for collective decisions.
Computational perspectives on the classical decision problem: a vade mecum
Bartosz Bednarczyk and Ian Pratt-Hartmann
The classical decision problem for first-order logic asks whether a given sentence of first-order logic is satisfiable, i.e. whether it true in some structure. While this problem is undecidable for first-order logic as a whole, its restrictions to certain fragments of first-order logic are known to admit of an effective solution. One of the central goals of research in mathematical logic in recent decades has been to determine the decidability and complexity of this problem for different fragments of first-order logic.
This course surveys major decidable fragments of first-order logic, including the two-variable, guarded, and fluted fragments, along with their extensions with counting quantifiers. These logics present different challenges, often requiring specialized techniques such as reduction to integer programming, small model constructions, tree decompositions, variable elimination, and reduction to tiling problems. We provide a comprehensive treatment of these techniques and briefly survey some open problems.
Introduction to Homotopy Type Theory / Univalent Foundations
Tom de Jong
Homotopy type theory (HoTT), also known as univalent foundations (UF), offers a modern foundation for mathematics and an alternative to traditional set theory. A salient feature of HoTT is the fact that it has been implemented in computer proof assistants, notably Agda and Rocq, which are tools that can verify proofs encoded by a user. HoTT is an extension of Martin-L\"of dependent type theory, but no familiarity with dependent type theory will be assumed. Instead, I will explain dependent type theory and the propositions-as-types interpretation to introduce and motivate univalent foundations. When it comes to HoTT, I will explain (1) its distinguishing features and techniques, like higher inductive types and the univalence axiom; (2) how to encode mathematics in it; and (3) illustrate the foregoing via examples in the Agda proof assistant.
Christoph Benzmüller and Luca Pasetto
The course provides an introduction to the LogiKEy framework and methodology for Logic and Knowledge Engineering. LogiKEy’s unifying approach is based on semantical embeddings of object logics in expressive classical higher-order logic (HOL). We begin with the methodology, introduce HOL, and give a guided practical tour of the Isabelle/HOL proof assistant. Next, we explain the technique of semantical embeddings of object logics in the meta-logic HOL, which enables the automation and model finding available in HOL provers to reason with the embedded logics. We then present two applications of the framework: (1) encoding deontic logics and corresponding ethical or legal theories to support computational tools for normative reasoning; and (2) the analysis of a version of the ontological argument from Kurt Gödel’s papers. We conclude with topics in knowledge representation within LogiKEy: combining logics, and encoding agents, actions, obligations, and knowledge. As a case study, we discuss the formalization of epistemic rights and present the embedding of a dynamic logic of the right to know in HOL.
Logic and Argumentation for New Generation AI
Leendert van der Torre and Liuwen Yu
Formal and computational argumentation has emerged as a central approach to logic in artificial intelligence (AI), providing foundations for computational logic, nonmonotonic logic, logic programming, conflict management, dispute resolution, inconsistent knowledge bases, games, dialogue, and decision making. Today’s new generation AI—characterized by agentic and neurosymbolic systems—calls for renewed logical perspectives on reasoning and interaction. This course discusses the bridge from classical to nonmonotonic logic and repositions argumentation as a core reasoning layer in agentic and neurosymbolic AI systems. We build on the foundations consolidated in the Handbook of Formal Argumentation (2018, 2021, 2024) and extend them with insights from the five-year national project “Logics for New Generation AI” (LNGAI, China, 2021–2025). Having evolved from our joint course at ZLAIRE (Zhejiang–Luxembourg Joint Lab on Advanced Intelligent Systems and Reasoning) and its updated version at NASSLLI 2024 (University of Washington, Seattle, USA), this new edition integrates feedback from both and brings these developments to the European logic community. The course welcomes students from logic, AI, computer science, philosophy, linguistics, and law interested in the logical foundations of next-generation AI.
Introduction to SAT and SMT solving
Karel Chvalovský and Mikoláš Janota
The propositional satisfiability (SAT) problem is not only a fundamental problem in logic and computation, but also a success story in computer science, with powerful solvers able to deal with complex industrial problems readily available. Moreover, it is possible to leverage the power of SAT solvers and combine them with various (decision) procedures (for arithmetic, arrays, bit vectors, etc.) in what is called satisfiability modulo theories (SMT). Powerful solvers for SMT are also available to help drive, for example, formal verification. In this course, we want to introduce the most important techniques used in modern SAT and SMT solvers. We will also discuss various challenges, including integrating machine learning (ML) techniques into fast solvers.
Foundational Courses
Coordination games, rationality, and logic
Valentin Goranko
This course is mainly about the theory of pure win-lose coordination games (WLC-games). These are simple, yet fundamental {strategic multi-player} games, in which all players have the common goal of coordinating, by selecting together a winning choice profile. If they succeed, everyone wins; else everyone loses. In general, coordination with no communication and conventions can become a highly non-trivial problem.
The course will first present the basic theory of WLC-games and will then extend it to coordination with structural conventions, coordination games with enriched structures, repeated coordination games, and probabilistic coordination. Finally, we will discuss applications of WLC-games to solving non-cooperative strategic form games and to strategic reasoning in multi-agent systems, and will present some formal logical systems for reasoning with, or about, coordination games.
The course will be accessible and appealing to a broad audience of students and researchers in philosophy, mathematics, computer science, and AI.
Foundational Course: First-Order Dynamic Logic
Shay Logan
This foundational course is an introduction to the syntax, semantics, proof-theory, and metatheory of first-order dynamic logic. It is meant to be accessible to anyone who knows how to write a proof. The course will be most accessible to someone who also has at some point seen soundness and completeness proofs for either first-order or modal logic of some sort. In order to make sure that there is some novelty in the course, we will also cover the less-typical "throughout", "during", and "preserves" modals.