Related papers: Game-theoretic Investigation of Intensional Equali…
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…
We present a new game semantics for Martin-L\"of type theory (MLTT), our aim is to give a mathematical and intensional explanation of MLTT. Specifically, we propose a category with families of a novel variant of games, which induces a…
In the present paper, based on the previous work (Part I), we present a game semantics for the intensional variant of intuitionistic type theory that refutes the principle of uniqueness of identity proofs and validates the univalence axiom,…
This work extends the present author's computational game semantics of Martin-L\"{o}f type theory to the cumulative hierarchy of universes. This extension completes game semantics of all standard types of Martin-L\"{o}f type theory for the…
We present a game semantics for intuitionistic type theory. Specifically, we propose categories with families of a new variant of games and strategies for both extensional and intensional variants of the type theory with dependent function,…
We prove consistency of intensional Martin-L\"of type theory (MLTT) with formal Church's thesis (CT), which was open for at least fifteen years. The difficulty in proving the consistency is that a standard method of realizability \`{a} la…
This paper presents a novel connection between homotopical algebra and mathematical logic. It is shown that a form of intensional type theory is valid in any Quillen model category, generalizing the Hofmann-Streicher groupoid model of…
We introduce versions of game-theoretic semantics (GTS) for Alternating-Time Temporal Logic (ATL). In GTS, truth is defined in terms of existence of a winning strategy in a semantic evaluation game, and thus the game-theoretic perspective…
We develop game-theoretic semantics (GTS) for the fragment ATL+ of the full Alternating-time Temporal Logic ATL*, essentially extending a recently introduced GTS for ATL. We first show that the new game-theoretic semantics is equivalent to…
We present a model of dependent type theory (DTT) with Pi-, 1-, Sigma- and intensional Id-types, which is based on a slight variation of the category of AJM-games and history-free winning strategies. The model satisfies Streicher's criteria…
Game semantics aim at describing the interactive behaviour of proofs by interpreting formulas as games on which proofs induce strategies. In this article, we introduce a game semantics for a fragment of first order propositional logic. One…
Game semantics extends the Curry-Howard isomorphism to a three-way correspondence: proofs, programs, strategies. But the universe of strategies goes beyond intuitionistic logics and lambda calculus, to capture stateful programs. In this…
Game semantics describe the interactive behavior of proofs by interpreting formulas as games on which proofs induce strategies. Such a semantics is introduced here for capturing dependencies induced by quantifications in first-order…
The probabilistic (or quantitative) modal mu-calculus is a fixed-point logic de- signed for expressing properties of probabilistic labeled transition systems (PLTS). Two semantics have been studied for this logic, both assigning to every…
This is an introductory textbook to univalent mathematics and homotopy type theory, a mathematical foundation that takes advantage of the structural nature of mathematical definitions and constructions. It is common in mathematical practice…
Genericity is the idea that the same program can work at many different data types. Longo, Milstead and Soloviev proposed to capture the inability of generic programs to probe the structure of their instances by the following equational…
Hyperproperties generalize traditional trace properties by relating multiple execution traces rather than reasoning about individual runs in isolation. They provide a unified way to express important requirements such as information flow…
Game semantics describe the interactive behavior of proofs by interpreting formulas as games on which proofs induce strategies. Such a semantics is introduced here for capturing dependencies induced by quantifications in first-order…
We define and develop two-level type theory (2LTT), a version of Martin-L\"of type theory which combines two different type theories. We refer to them as the inner and the outer type theory. In our case of interest, the inner theory is…
Advanced persistent threats (APT) combine a variety of different attack forms ranging from social engineering to technical exploits. The diversity and usual stealthiness of APT turns them into a central problem of contemporary practical…