Displaying similar documents to “Completeness, functional completeness and relative completeness.”

Four-Valued Logics BD and DM4: Expansions

Alexander S. Karpenko (2017)

Bulletin of the Section of Logic

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The paper discusses functional properties of some four-valued logics which are the expansions of four-valued Belnap’s logic DM4. At first, we consider the logics with two designated values, and then logics defined by matrices having the same underlying algebra, but with a different choice of designated values, i.e. with one designated value. In the preceding literature both approaches were developed independently. Moreover, we present the lattices of the functional expansions of DM4. ...

Functional Completeness in CPL via Correspondence Analysis

Dorota Leszczyńska-Jasion, Yaroslav Petrukhin, Vasilyi Shangin, Marcin Jukiewicz (2019)

Bulletin of the Section of Logic

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Kooi and Tamminga's correspondence analysis is a technique for designing proof systems, mostly, natural deduction and sequent systems. In this paper it is used to generate sequent calculi with invertible rules, whose only branching rule is the rule of cut. The calculi pertain to classical propositional logic and any of its fragments that may be obtained from adding a set (sets) of rules characterizing a two-argument Boolean function(s) to the negation fragment of classical propositional...

A 2-set-up Routley-Meyer Semantics for the 4-valued Relevant Logic E4

Gemma Robles, Sandra M. López, José M. Blanco, Marcos M. Recio, Jesús R. Paradela (2016)

Bulletin of the Section of Logic

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The logic BN4 can be considered as the 4-valued logic of the relevant conditional and the logic E4, as the 4-valued logic of (relevant) entailment. The aim of this paper is to endow E4 with a 2-set-up Routley-Meyer semantics. It is proved that E4 is strongly sound and complete w.r.t. this semantics.

Two Infinite Sequences of Pre-Maximal Extensions of the Relevant Logic E

Lidia Typańska-Czajka (2019)

Bulletin of the Section of Logic

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The only maximal extension of the logic of relevant entailment E is the classical logic CL. A logic L ⊆ [E,CL] called pre-maximal if and only if L is a coatom in the interval [E,CL]. We present two denumerable infinite sequences of premaximal extensions of the logic E. Note that for the relevant logic R there exist exactly three pre-maximal logics, i.e. coatoms in the interval [R,CL].

Useful Four-Valued Extension of the Temporal Logic KtT4

Vincent Degauquier (2018)

Bulletin of the Section of Logic

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The temporal logic KtT4 is the modal logic obtained from the minimal temporal logic Kt by requiring the accessibility relation to be reflexive (which corresponds to the axiom T) and transitive (which corresponds to the axiom 4). This article aims, firstly, at providing both a model-theoretic and a proof-theoretic characterisation of a four-valued extension of the temporal logic KtT4 and, secondly, at identifying some of the most useful properties of this extension in the context of partial...

Axiomatization of a Basic Logic of Logical Bilattices

Mitio Takano (2016)

Bulletin of the Section of Logic

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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.