Abstract
We provide non-deterministic semantics for the 3 basic paraconsistent C-systems C (also known as bC), Ci, and Cia, as well as to all 9 extensions of them by one or two of the schemata (l) ¬(φΛ¬φ) ⊃ ∘ φ and (e) φ ⊃ ¬¬φ. This includes da Costa’s original C 1 (which is equivalent to Cila). Our semantics is 3-valued for the systems without (l), and infinite-valued for the systems with it. We prove that these results cannot be improved: neither of the systems without (l) has either a finite characteristic ordinary matrix or a two-valued characteristic non-deterministic matrix, and neither of the systems with (l) has a finite characteristic non-deterministic matrix. Still, our semantics suffices for providing decision procedures for all the systems investigated.
This research was supported by THE ISRAEL SCIENCE FOUNDATION founded by The Israel Academy of Sciences and Humanities.
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Avron, A. (2005). Non-deterministic Semantics for Paraconsistent C-Systems. In: Godo, L. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2005. Lecture Notes in Computer Science(), vol 3571. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11518655_53
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DOI: https://doi.org/10.1007/11518655_53
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