Two Decision Procedures for da Costa’s $$C_n$$ Logics Based on Restricted Nmatrix Semantics

Coniglio, Marcelo E.; Toledo, Guilherme V.

doi:10.1007/s11225-021-09972-z

Cited by 15 publications

(19 citation statements)

References 26 publications

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“…We prove, already in [13], that RM Cn semantically characterizes C n and, furthermore, that its respective row-branching truth-table is a decision method for this logic.…”

Section: Rnmatrices For C Nmentioning

confidence: 66%

“…However, systems such as da Costa's C 1 , despite being decidable, can not be characterized even by a single finite Nmatrix ( [2]). In order to offer finite semantics of nondeterministic character for da Costa's hierarchy and other systems of similar difficulty, we have defined in [13] restricted non-deterministic matrices, alternatively called restricted Nmatrices or RNmatrices, independently defined by [33,34].…”

Section: Restricted Non-deterministic Matricesmentioning

confidence: 99%

“…In [13], we have constructed RNmatrices RM Cn = (A Cn , D n , F Cn ) for the calculi C n , trough use of swap structures, to achieve rather efficient decision methods for these logics. To give a brief summary of how this was achieved, consider the (n + 1)-tuples z = (z [1] , z [2] , .…”

Section: Rnmatrices For C Nmentioning

confidence: 99%

“…RNmatrices were also considered by Pawlowski and Urbaniak in the context of logics of informal provability ( [33,34]). In [13] we also show how several different semantical methodologies may be recast as RNmatrices, including Fidel and swap structures, bivaluations, static Nmatrices ( [3]), and PNmatrices ( [6,7]).…”

Section: Introductionmentioning

confidence: 99%

“…The most significative part of [13], however, was the construction of finite (n + 2-valued), manageable RNmatrices RM Cn capable of characterize C n . In particular, RM Cn are a perfect example of the cases in which RNmatrices induce a row-branching truth-table where one can algorithmically select those rows that correspond to unwanted homomorphisms, leading therefore to a decision method for its respective logic.…”

Section: Introductionmentioning

confidence: 99%

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Restricted swap structures for da Costa's $C_n$ and their category

Coniglio¹,

Toledo²

2021

Preprint

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In a previous article we introduced the concept of restricted Nmatrices (in short, RNmatrices), which generalize Nmatrices in the following sense: a RNmatrix is a Nmatrix together with a subset of valuations over it, from which the consequence relation is defined. Within this semantical framework we have characterized each paraconsistent logic C n in the hierarchy of da Costa by means of a (n + 2)-valued RNmatrix, which also provides a relatively simple decision procedure for each calculus (recalling that C 1 cannot be characterized by a single finite Nmatrix). In this paper we extend such RNmatrices for C n by means of what we call restricted swap-structures over arbitrary Boolean algebras, obtaining so a class of non-deterministic semantical structures which characterizes da Costa's systems. We give a brief algebraic and combinatorial description of the elements of the underlying RNmatrices.Finally, by presenting a notion of category of RNmatrices, we show that the category of RNmatrices for C n is in fact isomorphic to the category of non-trivial Boolean algebras.

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“…We prove, already in [13], that RM Cn semantically characterizes C n and, furthermore, that its respective row-branching truth-table is a decision method for this logic.…”

Section: Rnmatrices For C Nmentioning

confidence: 66%

Section: Restricted Non-deterministic Matricesmentioning

confidence: 99%

Section: Rnmatrices For C Nmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Restricted swap structures for da Costa's $C_n$ and their category

Coniglio¹,

Toledo²

2021

Preprint

Self Cite

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Effective Semantics for the Modal Logics K and KT via Non-deterministic Matrices

Lahav

Zohar

2022

Automated Reasoning

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A four-valued semantics for the modal logic K is introduced. Possible worlds are replaced by a hierarchy of four-valued valuations, where the valuations of the first level correspond to valuations that are legal w.r.t. a basic non-deterministic matrix, and each level further restricts its set of valuations. The semantics is proven to be effective, and to precisely capture derivations in a sequent calculus for K of a certain form. Similar results are then obtained for the modal logic KT, by simply deleting one of the truth values.

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