Related papers: Implementing program extraction from CL1-proofs
Temporal logic is a very powerful formalism deeply investigated and used in formal system design and verification. Its application usually reduces to solving specific decision problems such as model checking and satisfiability. In these…
Adding interaction to logic programming is an essential task. Expressive logics such as linear logic provide a theoretical basis for such a mechanism. Unfortunately, none of the existing linear logic languages can model interactions with…
The present paper introduces a novel notion of `(effective) computability', called viability, of strategies in game semantics in an intrinsic (i.e., without recourse to the standard Church-Turing computability), non-inductive and…
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…
This article presents an overview of computability logic -- the game-semantically constructed logic of interactive computational tasks and resources. There is only one non-overview, technical section in it, devoted to a proof of the…
Qualitative Choice Logic (QCL) and Conjunctive Choice Logic (CCL) are formalisms for preference handling, with especially QCL being well established in the field of AI. So far, analyses of these logics need to be done on a case-by-case…
The present work aims to give a unity of logic via standard sequential, unpolarized games. Specifically, our vision is that there must be mathematically precise concepts of linear refinement and intuitionistic restriction of logic such that…
A logical system derived from linear logic and called QMLL is introduced and shown able to capture all unitary quantum circuits. Conversely, any proof is shown to compute, through a concrete GoI interpretation, some quantum circuits. The…
Inductions and game semantics are two useful extensions to traditional logic programming. To be specific, inductions can capture a wider class of provable formulas in logic programming. Adopting game semantics can make logic programming…
Separation logic's compositionality and local reasoning properties have led to significant advances in scalable static analysis. But program analysis has new challenges -- many programs display computational effects and, orthogonally,…
There is a wide range of modal logics whose semantics goes beyond relational structures, and instead involves, e.g., probabilities, multi-player games, weights, or neighbourhood structures. Coalgebraic logic serves as a unifying semantic…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
We extend concurrent game structures (CGSs) with a simple notion of preference over computations and define a minimal notion of rationality for agents based on the concept of dominance. We use this notion to interpret a CL and an ATL…
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…
We advocate a declarative approach to proving properties of logic programs. Total correctness can be separated into correctness, completeness and clean termination; the latter includes non-floundering. Only clean termination depends on the…
We propose a novel logic, called Frame Logic (FL), that extends first-order logic (with recursive definitions) using a construct Sp(.) that captures the implicit supports of formulas -- the precise subset of the universe upon which their…
$\{log\}$ is a programming language at the intersection of Constraint Logic Programming, set programming and declarative programming. But $\{log\}$ is also a satisfiability solver for a theory of finite sets and finite binary relations.…
This paper presents matching logic, a first-order logic (FOL) variant for specifying and reasoning about structure by means of patterns and pattern matching. Its sentences, the patterns, are constructed using variables, symbols, connectives…
Coding theory revolves around the incorporation of redundancy into transmitted symbols, computation tasks, and stored data to guard against adversarial manipulation. However, error correction in coding theory is contingent upon a strict…
Reliably determining system trajectories is essential in many analysis and control design approaches. To this end, an initial value problem has to be usually solved via numerical algorithms which rely on a certain software realization.…