First-order logic and automated theorem proving (2nd ed.)
First-order logic and automated theorem proving (2nd ed.)
Quantification in Non-Deterministic Multi-Valued Structures
ISMVL '05 Proceedings of the 35th International Symposium on Multiple-Valued Logic
Non-deterministic Multiple-valued Structures
Journal of Logic and Computation
Non-deterministic semantics for logics with a consistency operator
International Journal of Approximate Reasoning
Modular Construction of Cut-free Sequent Calculi for Paraconsistent Logics
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
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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 C1*, 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.