Revisitando a Lógica de Dunn-Belnap

Blasio, Carolina

doi:10.1590/0100-6045.2017.v40n2.cb

Cited by 8 publications

(9 citation statements)

References 4 publications

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“…The two-dimensional presentation was also adopted in [12] to define predicate sequent systems for partial logics whose semantics is inferentially three-valued, and in [1] to define a propositional sequent system for an inferentially four-valued version of the logic of First Degree Entailment. In the present paper we have only dealt with specific logics in proving the second half of Theorem 12.…”

Section: Discussionmentioning

confidence: 99%

An Inferentially Many-Valued Two-Dimensional Notion of Entailment

2017

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Starting from the notions of q-entailment and p-entailment, a two-dimensional notion of entailment is developed with respect to certain generalized q-matrices referred to as B-matrices. After showing that every purely monotonic singleconclusion consequence relation is characterized by a class of B-matrices with respect to q-entailment as well as with respect to p-entailment, it is observed that, as a result, every such consequence relation has an inferentially four-valued characterization. Next, the canonical form of B-entailment, a two-dimensional multiple-conclusion notion of entailment based on B-matrices, is introduced, providing a uniform framework for studying several different notions of entailment based on designation, antidesignation, and their complements. Moreover, the two-dimensional concept of a B-consequence relation is defined, and an abstract characterization of such relations by classes of B-matrices is obtained. Finally, a contribution to the study of inferential many-valuedness is made by generalizing Suszko's Thesis and the corresponding reduction to show that any B-consequence relation is, in general, inferentially four-valued.An Inferentially Many-Valued Two-Dimensional Notion of Entailment 235 of a p-matrix [7,8]. A q-matrix (quasi matrix) is a structure A, D + , D − , where A is an algebra similar to a propositional language L, and where D + and D − are subsets of A, and D + ∩ D − = ∅. Usually, D + is referred to as the set of designated values and D − as the set of antidesignated values. A p-matrix (plausibility matrix) is a structure A, D + , D * , where A is an algebra similar to a propositional language L and D + ⊆ D * ⊆ A. The set D * is usually referred to as the set of plausible, non-antidesignated values.We adopt a compact notation that avoids superscripts and the barnotation for set-theoretic complementation, introducing the symbols Y, Y , N, and N to denote, respectively, the sets of designated, non-designated (V \ Y), antidesignated, and non-antidesignated (V \N) values. With a cognitive twist, they might be taken as representing acceptance, non-acceptance, rejection and non-rejection. 1

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Section: Discussionmentioning

confidence: 99%

An Inferentially Many-Valued Two-Dimensional Notion of Entailment

2017

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“…One may readily see that these interpretations correspond to the ones of First Degree Entailment and that this B PN Σ FDEmatrix corresponds to the logic E B presented in [7].…”

Section: Example 2 Letmentioning

confidence: 86%

“…It is straightforward to check that (see [7]): • I that interprets the latter connectives according to the following (non-deterministic) truth-tables (here and below, braces will be omitted from the images of the interpretations):…”

Section: Two-dimensional Non-deterministic Matricesmentioning

confidence: 99%

“…The aforementioned inference, for instance, would be expressed by the two-dimensional judgment ∅ ∅ | A A→B , which is intended to enforce that an agent is not expected to find reasons for rejecting A → B while failing to find reasons for accepting A. From a semantical standpoint, the latter notion of consequence may be induced by a two-dimensional logical matrix [7,9], whose associated two-dimensional canonical entailment relation very naturally embraces bilateralism and involves two possibly distinct collections of distinguished truth-values: the 'designated' values and the 'anti-designated' values, respectively equated with acceptance and rejection.…”

Section: Introductionmentioning

confidence: 99%

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Proof Search on Bilateralist Judgments over Non-deterministic Semantics

Greati¹,

Marcelino²,

Marcos³

2021

Preprint

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The bilateralist approach to logical consequence maintains that judgments of different qualities should be taken into account in determining what-follows-from-what. We argue that such an approach may be actualized by a two-dimensional notion of entailment induced by semantic structures that also accommodate non-deterministic and partial interpretations, and propose a prooftheoretical apparatus to reason over bilateralist judgments using symmetrical two-dimensional analytical Hilbert-style calculi. We also provide a proof-search algorithm for finite analytic calculi that runs in at most exponential time, in general, and in polynomial time when only rules having at most one formula in the succedent are present in the concerned calculus.

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“…A different identity criterion is evaluated, in Section 5, 1 Essentially, B-matrices are algebraic structures which generalize regular logical matrices, in that they do not present an algebra with a distinguished set of designated elements, but rather with two distinguished sets-one of accepted and one of rejected elements. For a more detailed discussion of these results, see [5] and [6].…”

Section: Introductionmentioning

confidence: 96%

(Meta)inferential levels of entailment beyond the Tarskian paradigm

2019

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In this paper we discuss the extent to which the very existence of substructural logics puts the Tarskian conception of logical systems in jeopardy. In order to do this, we highlight the importance of the presence of different levels of entailment in a given logic, looking not only at inferences between collections of formulae but also at inferences between collections of inferences-and more. We discuss appropriate refinements or modifications of the usual Tarskian identity criterion for logical systems, and propose an alternative of our own. After that, we consider a number of objections to our account and evaluate a substantially different approach to the same problem.

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Revisitando a Lógica de Dunn-Belnap

Cited by 8 publications

References 4 publications

An Inferentially Many-Valued Two-Dimensional Notion of Entailment

An Inferentially Many-Valued Two-Dimensional Notion of Entailment

Proof Search on Bilateralist Judgments over Non-deterministic Semantics

(Meta)inferential levels of entailment beyond the Tarskian paradigm

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