4 research outputs found
Adding an Implication to Logics of Perfect Paradefinite Algebras
Perfect paradefinite algebras are De Morgan algebras expanded with a
perfection (or classicality) operation. They form a variety that is
term-equivalent to the variety of involutive Stone algebras. Their associated
multiple-conclusion (Set-Set) and single-conclusion (Set-Fmla) order-preserving
logics are non-algebraizable self-extensional logics of formal inconsistency
and undeterminedness determined by a six-valued matrix, studied in depth by
Gomes et al. (2022) from both the algebraic and the proof-theoretical
perspectives. We continue hereby that study by investigating directions for
conservatively expanding these logics with an implication connective
(essentially, one that admits the deduction-detachment theorem). We first
consider logics given by very simple and manageable non-deterministic semantics
whose implication (in isolation) is classical. These, nevertheless, fail to be
self-extensional. We then consider the implication realized by the relative
pseudo-complement over the six-valued perfect paradefinite algebra. Our
strategy is to expand such algebra with this connective and study the
(self-extensional) Set-Set and Set-Fmla order-preserving logics, as well as the
T-assertional logics of the variety induced by the new algebra. We provide
axiomatizations for such new variety and for such logics, drawing parallels
with the class of symmetric Heyting algebras and with Moisil's `symmetric modal
logic'. For the Set-Set logic, in particular, the axiomatization we obtain is
analytic. We close by studying interpolation properties for these logics and
concluding that the new variety has the Maehara amalgamation property
Automated Reasoning
This volume, LNAI 13385, constitutes the refereed proceedings of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, held in Haifa, Israel, in August 2022. The 32 full research papers and 9 short papers presented together with two invited talks were carefully reviewed and selected from 85 submissions. The papers focus on the following topics: Satisfiability, SMT Solving,Arithmetic; Calculi and Orderings; Knowledge Representation and Jutsification; Choices, Invariance, Substitutions and Formalization; Modal Logics; Proofs System and Proofs Search; Evolution, Termination and Decision Prolems. This is an open access book