Related papers: Game semantics for the constructive $\mu$-calculus
The classical propositional logic is known to be sound and complete with respect to the set semantics that interprets connectives as set operations. The paper extends propositional language by a new binary modality that corresponds to…
We define a semantics for first-order logic with generalized quantifiers based on double teams. We also define and investigate a notion of a generalized atom. Such atoms can be used in order to define extensions of first-order logic with a…
Formal models of games help us account for and predict behavior, leading to more robust and innovative designs. While the games research community has proposed many formalisms for both the "game half" (game models, game description…
$\mu$-Calculus and automata on infinite trees are complementary ways of describing infinite tree languages. The correspondence between $\mu$-Calculus and alternating tree automaton is used to solve the satisfiability and model checking…
In this work, we present a logic based on first-order CTL, namely Game Analysis Logic (GAL), in order to reason about games. We relate models and solution concepts of Game Theory as models and formulas of GAL, respectively. Precisely, we…
We study the expressive power of various modal logics with team semantics. We show that exactly the properties of teams that are downward closed and closed under team k-bisimulation, for some finite k, are definable in modal logic extended…
This paper presents a soundness and completeness proof for propositional intuitionistic calculus with respect to the semantics of computability logic. The latter interprets formulas as interactive computational problems, formalized as games…
In the same sense as classical logic is a formal theory of truth, the recently initiated approach called computability logic is a formal theory of computability. It understands (interactive) computational problems as games played by a…
We present new game semantics of Martin-L\"of type theory (MLTT) equipped with One-, Zero-, N-, Pi-, Sigma- and Id-types. Our game semantics interprets MLTT more accurately than existing ones. Another advantage of our game semantics over…
In this paper we provide a unifying description of different types of semantics of modal logic found in the literature via the framework of topological categories. In the style of categorical logic, we establish an exact correspondence…
We extend the {\lambda}-calculus with constructs suitable for relational and functional-logic programming: non-deterministic choice, fresh variable introduction, and unification of expressions. In order to be able to unify…
In this paper, we define a new realizability semantics for the simply typed lambda-mu-calculus. We show that if a term is typable, then it inhabits the interpretation of its type. We also prove a completeness result of our realizability…
Ehrenfeucht-Fra\"iss\'e games provide a fundamental method for proving elementary equivalence (and equivalence up to a certain quantifier rank) of relational structures. We investigate the soundness and completeness of this method in the…
Game theory is used by all behavioral sciences, but its development has long centered around tools for relatively simple games and toy systems, such as the economic interpretation of equilibrium outcomes. Our contribution, compositional…
We show that the model-checking problem is decidable for a fragment of the epistemic \mu-calculus. The fragment allows free variables within the scope of epistemic modalities in a restricted form that avoids constructing formulas embodying…
Combinatorial games are widely used in finite model theory, constraint satisfaction, modal logic and concurrency theory to characterize logical equivalences between structures. In particular, Ehrenfeucht-Fraisse games, pebble games, and…
Proofs, in Ludics, have an interpretation provided by their counter-proofs, that is the objects they interact with. We follow the same idea by proposing that sentence meanings are given by the counter-meanings they are opposed to in a…
Choice constructs are an important part of the language of logic programming, yet the study of their semantics has been a challenging task. So far, only two-valued semantics have been studied, and the different proposals for such semantics…
This paper contributes to the theory of the modal $\mu$-calculus by proving some model-theoretic results. More in particular, we discuss a number of semantic properties pertaining to formulas of the modal $\mu$-calculus. For each of these…
We define sound and adequate denotational and operational semantics for the stochastic lambda calculus. These two semantic approaches build on previous work that used similar techniques to reason about higher-order probabilistic programs,…