Related papers: Defining implication relation for classical logic

Human communication is based on a variety of inferences that we draw from sentences, often going beyond what is literally said. While there is wide agreement on the basic distinction between entailment, implicature, and presupposition, the…

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…

It is standard to regard the intuitionistic restriction of a classical logic as increasing the expressivity of the logic because the classical logic can be adequately represented in the intuitionistic logic by double-negation, while the…

This article presents a computational semantics for classical logic using constructive type theory. Such semantics seems impossible because classical logic allows the Law of Excluded Middle (LEM), not accepted in constructive logic since it…

We propose a new calculus SCL(EQ) for first-order logic with equality that only learns non-redundant clauses. Following the idea of CDCL (Conflict Driven Clause Learning) and SCL (Clause Learning from Simple Models) a ground literal model…

Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a recently launched program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth that logic has more traditionally…

This paper extends implication-space semantics to include first-order quantification. Implication-space semantics has recently been introduced as an inferentialist formal semantics that can capture nonmonotonic and nontransitive material…

This paper defines a new proof- and category-theoretic framework for classical linear logic that separates reasoning into one linear regime and two persistent regimes corresponding to ! and ?. The resulting linear/producer/consumer (LPC)…

In this paper we will see deductive systems for classical propositional and predicate logic in the calculus of structures. Like sequent systems, they have a cut rule which is admissible. In addition, they enjoy a top-down symmetry and some…

We present a proof-theoretical study of the interpretability logic IL, providing a wellfounded and a non-wellfounded sequent calculus for IL. The non-wellfounded calculus is used to establish a cut elimination argument for both calculi. In…

We introduce Craig interpolation and related notions such as uniform interpolation, Beth definability, and theory decomposition in classical propositional logic. We present four approaches to computing interpolants: via quantifier…

We give a novel approach to proving soundness and completeness for a logic (henceforth: the object-logic) that bypasses truth-in-a-model to work directly with validity. Instead of working with specific worlds in specific models, we reason…

The Boolean logic of subsets, usually presented as `propositional logic,' is considered as being "classical" while intuitionistic logic and the many sublogics and off-shoots are "non-classical." But there is another mathematical logic, the…

We examine the interplay between projectivity (in the sense that was introduced by S.~Ghilardi) and uniform post-interpolant for the classical and intuitionistic propositional logic. More precisely, we explore whether a projective…

We propose a new version of generalized probabilistic propositional logic, namely, discrete-continuous logic (DCL) in which every generalized proposition (GP) is represented as 2x2 nondiagonal positive matrix with unit trace. We demonstrate…

Linear logic (LL) is a resource-aware, abstract logic programming language that refines both classical and intuitionistic logic. Linear logic semantics is typically presented in one of two ways: by associating each formula with the set of…

To appear in Theory and Practice of Logic Programming (TPLP). In this paper we propose an extension of logic programming (LP) where each default literal derived from the well-founded model is associated to a justification represented as an…

This paper continues an established line of research about the relations between argumentation theory, particularly assumption-based argumentation, and different kinds of logic programs. In particular, we extend known result of Caminada,…

We consider a proper propositional quantum logic and show that it has multiple disjoint lattice models, only one of which is an orthomodular lattice (algebra) underlying Hilbert (quantum) space. We give an equivalent proof for the classical…

Belnap-Dunn logic, also knows as the logic of First-Degree Entailment, is a logic that can serve as the underlying logic of theories that are inconsistent or incomplete. For various reasons, different expansions of Belnap-Dunn logic with…