76 research outputs found
Axiomatization of a Basic Logic of Logical Bilattices
A sequential axiomatization is given for the 16-valued logic that has been proposed by Shramko-Wansing (J Philos Logic 34:121–153, 2005) as a candidate for the basic logic of logical bilattices
Track-Down Operations on Bilattices
This paper discusses a dualization of Fitting's notion of a "cut-down" operation on a bilattice, rendering a "track-down" operation, later used to represent the idea that a consistent opinion cannot arise from a set including an inconsistent opinion. The logic of track-down operations on bilattices is proved equivalent to the logic d_Sfde, dual to Deutsch's system S_fde. Furthermore, track-down operations are employed to provide an epistemic interpretation for paraconsistent weak Kleene logic. Finally, two logics of sequential combinations of cut-and track-down operations allow settling positively the question of whether bilattice-based semantics are available for subsystems of S_fde
Semantic Incompleteness of Hilbert System for a Combination of Classical and Intuitionistic Propositional Logic
This paper shows Hilbert system , given by del Cerro and
Herzig (1996) is semantically incomplete. This system is proposed as a proof
theory for Kripke semantics for a combination of intuitionistic and classical
propositional logic, which is obtained by adding the natural semantic clause of
classical implication into intuitionistic Kripke semantics. Although Hilbert
system contains intuitionistic modus ponens as a rule, it
does not contain classical modus ponens. This paper gives an argument ensuring
that the system is semantically incomplete because of the
absence of classical modus ponens. Our method is based on the logic of paradox,
which is a paraconsistent logic proposed by Priest (1979).Comment: 9 page
Free Quantification in Four-Valued and Fuzzy Bilattice-Valued Logics
We introduce a variant of free logic (i.e., a logic admitting terms with
nonexistent referents) that accommodates truth-value gluts as well as gaps.
Employing a suitable expansion of the Belnap--Dunn four-valued logic, we
specify a dual-domain semantics for free logic, in which propositions
containing non-denoting terms can be true, false, neither true nor false, or
both true and false. In each model, the dual domain semantics separates
existing and non-existing objects into two subdomains, making it possible to
quantify either over all objects or existing objects only. We also outline a
fuzzy variant of the dual-domain semantics, accommodating non-denoting terms in
fuzzy contexts that can be partially indeterminate or inconsistent.Comment: 12 pages, submitted to IUKM 2023 Conferenc
Symmetric and dual paraconsistent logics
Two new first-order paraconsistent logics with De Morgan-type negations and co-implication, called symmetric paraconsistent logic (SPL) and dual paraconsistent logic (DPL), are introduced as Gentzen-type sequent calculi. The logic SPL is symmetric in the sense that the rule of contraposition is admissible in cut-free SPL. By using this symmetry property, a simpler cut-free sequent calculus for SPL is obtained. The logic DPL is not symmetric, but it has the duality principle. Simple semantics for SPL and DPL are introduced, and the completeness theorems with respect to these semantics are proved. The cut-elimination theorems for SPL and DPL are proved in two ways: One is a syntactical way which is based on the embedding theorems of SPL and DPL into Gentzen’s LK, and the other is a semantical way which is based on the completeness theorems
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