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A deductive system is structurally complete if its admissible inference rules are derivable. For several important systems, like modal logic S5, failure of structural completeness is caused only by the underivability of passive rules, i.e.…
Saturation is a fundamental game-semantic property satisfied by strategies that interpret higher-order concurrent programs. It states that the strategy must be closed under certain rearrangements of moves, and corresponds to the intuition…
Arboreal categories provide an axiomatic framework in which abstract notions of bisimilarity and back-and-forth games can be defined. They act on extensional categories, typically consisting of relational structures, via arboreal…
This paper deals with strong structural controllability of linear systems. In contrast to existing work, the structured systems studied in this paper have a so-called zero/nonzero/arbitrary structure, which means that some of the entries…
We investigate combinations of structures by families of structures relative to families of unary predicates and equivalence relations. Conditions preserving $\omega$-categoricity and Ehrenfeuchtness under these combinations are…
The back-and-forth relations $M\leq_\alpha N$ are central to computable structure theory and countable model theory. It is well-known that the relation $\{(M,N) : M \leq_\alpha N\}$ is (lightface) $\Pi^0_{2\alpha}$. We show that this is…
We give a sufficient condition for Kripke completeness of modal logics enriched with the transitive closure modality. More precisely, we show that if a logic admits what we call definable filtration (ADF), then such an expansion of the…
Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…
We give several characterizations of when a complete first-order theory $T$ is monadically NIP, i.e. when expansions of $T$ by arbitrary unary predicates do not have the independence property. The central characterization is a condition on…
We consider finite-horizon and infinite-horizon versions of a dynamic game with $N$ selfish players who observe their types privately and take actions that are publicly observed. Players' types evolve as conditionally independent Markov…
This paper presents preliminary work on a general system for integrating dependent types into substructural type systems such as linear logic and linear type theory. Prior work on this front has generally managed to deliver type systems…
Conditionals play a key role in different areas of logic and probabilistic reasoning, and they have been studied and formalized from different angles. In this paper we focus on the de Finetti's notion of conditional as a three-valued…
We consider a hierarchy of four typed call-by-value languages with either higher-order or ground-type references and with either callcc or no control operator.Our first result is a fully abstract trace model for the most expressive setting,…
The theory of finitely supported algebraic structures represents a reformulation of Zermelo-Fraenkel set theory in which every construction is finitely supported according to the action of a group of permutations of some basic elements…
In an interactive belief model, are the players "commonly meta-certain" of the model itself? This paper formalizes such implicit "common meta-certainty" assumption. To that end, the paper expands the objects of players' beliefs from events…
Curry-style system F, ie. system F with no explicit types in terms, can be seen as a core presentation of polymorphism from the point of view of programming languages. This paper gives a characterisation of type isomorphisms for this…
We characterize those intersection-type theories which yield complete intersection-type assignment systems for lambda-calculi, with respect to the three canonical set-theoretical semantics for intersection-types: the inference semantics,…
We use type-theoretic techniques to present an algebraic theory of $\infty$-categories with strict units. Starting with a known type-theoretic presentation of fully weak $\infty$-categories, in which terms denote valid operations, we extend…
We propose a multi-scale extension of conformal prediction, an approach that constructs prediction sets with finite-sample coverage guarantees under minimal statistical assumptions. Classic conformal prediction relies on a single notion of…
Incomplete cooperative games generalise the classical model of cooperative games by omitting the values of some of the coalitions. This allows to incorporate uncertainty into the model and study the underlying games as well as possible…