Non-Deterministic Semantics for First-order Paraconsistent Logics

Anna Zamansky, Arnon Avron

Using non-deterministic structures called Nmatrices, we provide simple modular non-deterministic semantics for a large family of first-order paraconsistent logics with a formal consistency operator, also known as LFIs. This includes da-Costa's well known predicate calculus C*1. We show how consistency propagation in quantified formulas is captured in the semantic framework of Nmatrices, and analyze the semantic effects of different styles of propagation considered in the literature of LFIs. Then we demonstrate how the tool of Nmatrices can be applied to prove a non-trivial property of first-order LFIs discussed in this paper.

Subjects: 3. Automated Reasoning; 5. Common Sense Reasoning

Submitted: Mar 6, 2006

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