Twist-structures semantics for the logics of the hierarchy InPk

Ramos, Fernando Maciel; Fernández, Vı́ctor

doi:10.3166/jancl.19.183-209

Cited by 7 publications

(6 citation statements)

References 10 publications

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“…Aferwards, twist structures semantics have been generalized in the literature to several classes of logics, including modal logics (see, for instance, [29,30,32]). In all the cases, each twist structure N have associated a logical matrix M(N ) = (N , D N ) defined as above.…”

Section: From Kalman-cignoli Construction To Fidel-vakarelov Twist Stmentioning

confidence: 99%

Non-deterministic algebraization of logics by swap structures1

Coniglio

Figallo-Orellano

Golzio

2018

Logic Journal of the IGPL

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Multialgebras (or hyperalgebras, or non-deterministic algebras) have been very much studied in Mathematics and in Computer Science. In 2016 Carnielli and Coniglio introduced a class of multialgebras called swap structures, as a semantic framework for dealing with several logics of formal inconsistency (or LFIs) which cannot be semantically characterized by a single finite matrix. In particular, these LFIs are not algebraizable by the standard tools of abstract algebraic logic. In this paper, the first steps towards a theory of non-deterministic algebraization of logics by swap structures are given. Specifically, a formal study of swap structures for LFIs is developed, by adapting concepts of universal algebra to multialgebras in a suitable way. A decomposition theorem similar to Birkhoff's representation theorem is obtained for each class of swap structures. Moreover, when applied to the 3-valued algebraizable logic J3 the usual class of algebraic models is recovered, and the swap structures semantics became twist-structures semantics (as introduced by Fidel-Vakarelov). This fact, together with the existence of a functor from the category of Boolean algebras to the category of swap structures for each LFI, which is closely connected with Kalman's functor, suggests that swap structures can be considered as non-deterministic twist structures, opening so interesting possibilities for dealing with non-algebraizable logics by means of multialgebraic semantics.

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Section: From Kalman-cignoli Construction To Fidel-vakarelov Twist Stmentioning

confidence: 99%

Non-deterministic algebraization of logics by swap structures1

Coniglio

Figallo-Orellano

Golzio

2018

Logic Journal of the IGPL

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“…We will characterize the tautologies of I 1 P 0 using discriminant structures, whose definition will be given in the sequel. This characterization (with some little changes) was shown in [8]. For our purposes we are based on Boolean algebras of the form B = (B, C B ) (recall Definition 1.3): Definition 2.2.…”

Section: Discriminant Structure Semantics: Some Motivating Examplesmentioning

confidence: 99%

“…It is usually accepted that the constructions known as Twist-Structure Semantics appeared in the works (done in an independent way) of M. Fidel and D. Vakarelov, to provide an alternative semantics for Nelson Intuitionistic Logic with Strong Negation (see [6] and [15]). Nowadays, the constructions developed in these papers were adapted to a great number of logics (see [7], [8] or [9], for example). Thus, Twist-Structure Semantics are an object of numerous, deep and fruitful investigations.…”

Section: Relations With Dyadic and Twist-structure Semanticsmentioning

confidence: 99%

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Discriminant Structures Associated to Matrix Semantics

Fernández¹,

Murciano²

2018

rev.colomb.mat

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In this paper we show a method to characterize logical matrices by means of a special kind of structures, called here discriminant structures for this purpose. Its deﬁnition is based on the discrimination of each truthvalue of a given (ﬁnite) matrix M = (A, D), w.r.t. its belonging to D. From this starting point, we deﬁne a whole class SM of discriminant structures. This class is characterized by a set of Boolean equations, as it is shown here. In addition, several technical results are presented, and it is emphasized the relation of the Discriminant Structures Semantics (D.S.S) with other related semantics such as Dyadic or Twist-Structure.

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“…Then in [19] it was proved that Nelson's paraconsistent logic N4 can be characterised using twist-structures over implicative lattices, and that the abstract closure of the class of these structures forms a variety. 3 Other examples of application of twist-structures may be found in [28] and [23].…”

Section: Introductionmentioning

confidence: 99%

The lattice of Belnapian modal logics: Special extensions and counterparts

Odintsov

Speranski

2016

LLP

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Let K be the least normal modal logic and BK its Belnapian version, which enriches K with 'strong negation'. We carry out a systematic study of the lattice of logics containing BK based on: • introducing the classes (or rather sublattices) of so-called explosive, complete and classical Belnapian modal logics; • assigning to every normal modal logic three special conservative extensions in these classes; • associating with every Belnapian modal logic its explosive, complete and classical counterparts. We investigate the relationships between special extensions and counterparts, provide certain handy characterisations and suggest a useful decomposition of the lattice of logics containing BK.

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Twist-structures semantics for the logics of the hierarchy IⁿP^k

Cited by 7 publications

References 10 publications

Non-deterministic algebraization of logics by swap structures1

Non-deterministic algebraization of logics by swap structures1

Discriminant Structures Associated to Matrix Semantics

The lattice of Belnapian modal logics: Special extensions and counterparts

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