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Effective Non-deterministic Semantics for First-order LFIs

A paraconsistent logic is a logic which allows non-trivial inconsistent theories. One of the best-known approaches to designing useful paraconsistent logics is da Costa’s approach, which has led to the family of Logics of Formal Inconsistency (LFIs), where the notion of inconsistency is expressed at the object level. In this paper we use non-deterministic matrices, a generalization of standard multi-valued matrices, to provide simple and modular finite-valued semantics for a large family of first-order LFIs. We demonstrate that the modular approach of Nmatrices provides new insights into the semantic role of the studied axioms and the dependencies between them. Furthermore, we study the issue of effectiveness in Nmatrices, a property which is crucial for the usefulness of semantics. We show that all of the nondeterministic semantics provided in this paper are effective.