Related papers: Characterization of Strongly Equivalent Logic Prog…

Linear Logic refines Intuitionnistic Logic by taking into account the resources used during the proof and program computation. In the past decades, it has been extended to various frameworks. The most famous are indexed linear logics which…

The fact that classical mathematical proofs of simply existential statements can be read as programs was established by Goedel and Kreisel half a century ago. But the possibility of extracting useful computational content from classical…

We consider a family of two-valued "fully evaluated left-sequential logics" (FELs), of which Free FEL (defined by Staudt in 2012) is most distinguishing (weakest) and immune to atomic side effects. Next is Memorising FEL, in which…

In the theory of answer set programming, two groups of rules are called strongly equivalent if, informally speaking, they have the same meaning in any context. The relationship between strong equivalence and the propositional logic of…

We extend the framework of abstract algebraic logic to weak logics, namely logical systems which are not necessarily closed under uniform substitution. We interpret weak logics by algebras expanded with an additional predicate and we…

Programs with a continuous state space or that interact with physical processes often require notions of equivalence going beyond the standard binary setting in which equivalence either holds or does not hold. In this paper we explore the…

We introduce a sequent calculus for the propositional team logic with both the split disjunction and the inquisitive disjunction consisting of a Gentzen-style system (G3-like) for classical propositional logic together with two…

Cathoristic logic is a multi-modal logic where negation is replaced by a novel operator allowing the expression of incompatible sentences. We present the syntax and semantics of the logic including complete proof rules, and establish a…

An uninterpreted program (UP) is a program whose semantics is defined over the theory of uninterpreted functions. This is a common abstraction used in equivalence checking, compiler optimization, and program verification. While simple, the…

Probabilistic logic programs are logic programs where some facts hold with a specified probability. Here, we investigate these programs with a causal framework that allows counterfactual queries. Learning the program structure from…

The KLM approach to defeasible reasoning introduces a weakened form of implication into classical logic. This allows one to incorporate exceptions to general rules into a logical system, and for old conclusions to be withdrawn upon learning…

The logic embedding tool provides a procedural encoding for non-classical reasoning problems into classical higher-order logic. It is extensible and can support an increasing number of different non-classical logics as reasoning targets.…

The stable model semantics had been recently generalized to non-Herbrand structures by several works, which provides a unified framework and solid logical foundations for answer set programming. This paper focuses on the expressiveness of…

This paper introduces a notion of equivalence for higher-dimensional automata, called weak equivalence. Weak equivalence focuses mainly on a traditional trace language and a new homology language, which captures the overall independence…

The modal systems S1--S3 were introduced by C. I. Lewis as logics for strict implication. While there are Kripke semantics for S2 and S3, there is no known natural semantics for S1. We extend S1 by a Substitution Principle SP which…

This paper generalizes the encoding of argumentation frameworks beyond the classical 2-valued propositional logic system ($PL_2$) to 3-valued propositional logic systems ($PL_3$s) and fuzzy propositional logic systems ($PL_{[0,1]}s$),…

Weak memory models specify the semantics of concurrent programs on multi-core architectures. Reasoning techniques for weak memory models are often specialized to one fixed model and verification results are hence not transferable to other…

In this study, we study weak values from a quantum-logical viewpoint. In addition, we examine the validity of the counterfactual statements of Hardy's paradox, which are based on weak values, and we show that these statements have not been…

In this paper, we facilitate the reasoning about impure programming languages, by annotating terms with `decorations' that describe what computational (side) effect evaluation of a term may involve. In a point-free categorical…

In this paper we prove that three of the main propositional logics of dependence (including propositional dependence logic and inquisitive logic), none of which is structural, are structurally complete with respect to a class of…