Quantification in Non-Deterministic Multi-Valued Structures

Lecture Notes in Computer Science

2011

Section: Matrix-based (Kripke) Semanticsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Basic Constructive Connectives, Determinism and Matrix-Based Semantics

Ciabattoni

Lahav

Lecture Notes in Computer Science

2011

“…Our main semantic tool in what follows will be the following generalization of the concept of a multi-valued matrix given in [1,2,3,21,20]. …”

Section: Non-deterministic Matricesmentioning

confidence: 99%

“…An alternative framework for providing semantics for propositional paraconsistent logics was introduced in [1] (and used in [2,3,4]). This framework uses a generalization of the standard multi-valued matrices, called non-deterministic matrices (Nmatrices).…”

Section: Introductionmentioning

confidence: 99%

Many-Valued Non-deterministic Semantics for First-Order Logics of Formal (In)consistency

Avron

Lecture Notes in Computer Science

2007

Abstract.A paraconsistent logic is a logic which allows non-trivial inconsistent theories. One of the oldest and best known approaches to the problem of designing useful paraconsistent logics is da Costa's approach, which seeks to allow the use of classical logic whenever it is safe to do so, but behaves completely differently when contradictions are involved. da Costa's approach has led to the family of Logics of Formal (In)consistency (LFIs). In this paper we provide non-deterministic semantics for a very large family of first-order LFIs (which includes da Costa's original system C * 1 , as well as thousands of other logics). We show that our semantics is effective and modular, and we use this effectiveness to derive some important properties of logics in this family.

Canonical Gentzen-Type Calculi with (n,k)-ary Quantifiers

Avron

2006

Automated Reasoning

Abstract. Propositional canonical Gentzen-type systems, introduced in [1], are systems which in addition to the standard axioms and structural rules have only logical rules in which exactly one occurrence of a connective is introduced and no other connective is mentioned.[1] provides a constructive coherence criterion for the non-triviality of such systems and shows that a system of this kind admits cut-elimination iff it is coherent. The semantics of such systems is provided by two-valued nondeterministic matrices (2Nmatrices).[3] extends these results to systems with unary quantifiers of a very restricted form. In this paper we substantially extend the characterization of canonical systems to (n, k)-ary quantifiers, which bind k distinct variables and connect n formulas. We show that the coherence criterion remains constructive for such systems, and that for the case of k ∈ {0, 1}: (i) a canonical system is coherent iff it has a strongly characteristic 2Nmatrix, and (ii) if a canonical system is coherent, then it admits cut-elimination.