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Maximal and premaximal paraconsistency in the framework of threevalued semantics
 STUDIA LOGICA,
, 2011
"... Maximality is a desirable property of paraconsistent logics, motivated by the aspiration to tolerate inconsistencies, but at the same time retain from classical logic as much as possible. In this paper we introduce the strongest possible notion of maximal paraconsistency, and investigate it in the c ..."
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Cited by 4 (2 self)
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of all possible paraconsistent determinizations of a nondeterministic matrix, thus representing what is really essential for their maximal paraconsistency.
5valued Nondeterministic Semantics for The Basic Paraconsistent Logic mCi
, 2008
"... One of the most important paraconsistent logics is the logic mCi, which is one of the two basic logics of formal inconsistency. In this paper we present a 5valued characteristic nondeterministic matrix for mCi. This provides a quite nontrivial example for the utility and effectiveness of the use o ..."
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Cited by 4 (3 self)
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One of the most important paraconsistent logics is the logic mCi, which is one of the two basic logics of formal inconsistency. In this paper we present a 5valued characteristic nondeterministic matrix for mCi. This provides a quite nontrivial example for the utility and effectiveness of the use
Matrix Semantics for Annotated Logics
 Models, Algebras, and Proofs, Proceedings of the X SLALM
, 1995
"... Abstract. A matrix semantics for paraconsistent systems SALτ of annotated logics is developed. Systems SALτ are extensions of the systems Pτ S, previously proven algebraizable by the authors. The results reported here will be useful in the study of the class of algebras that arise in the process of ..."
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Cited by 4 (4 self)
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Abstract. A matrix semantics for paraconsistent systems SALτ of annotated logics is developed. Systems SALτ are extensions of the systems Pτ S, previously proven algebraizable by the authors. The results reported here will be useful in the study of the class of algebras that arise in the process
An Annotated Logic Defined by a Matrix
"... Of special interest in abstract algebraic logic currently is the problem of extending the general theory of algebraization to logical systems that fail to be structural. The annotated logics PL were introduced in the late eighties as a logical framework to deal with deductive databases that contain ..."
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Cited by 3 (3 self)
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inconsistent, conicting or contradictory information. Like many paraconsistent logics they are nonstructural, and for this reason they do not have an algebraic semantics in the usual sense. In this paper a structural and algebraizable annotated logic PM(L) is constructed that simulates the deductive process
Pontificia Universidad Católica de Chile. Funding for the second author has been provided
"... Literal paraconsistent–paracomplete matrices, or LPP–matrices, were introduced in [2] in an attempt to give a meaningful semantics, via the classic method of matrices, to a large family of paraconsistent and paracomplete logics. The main characteristic of these logics is that paraconsistency and/or ..."
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and formalizations. Literal–Paraconsistent–Paracomplete Matrices Let A be a set such that {0, 1} ⊆ A, F ⊆ A such that 1 ∈ F and 0 / ∈ F, and ∼ : P − → P a function such that ∼ 1 = 0 and ∼ 0 = 1. A literal–paraconsistent–paracomplete matrix, or LPP–matrix, 〈A, F 〉 that has the unary operation ∼ and three binary
Nondeterministic Semantics for Logics with a Consistency Operator
 IN THE INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
, 2006
"... In order to handle inconsistent knowledge bases in a reasonable way, one needs a logic which allows nontrivial inconsistent theories. Logics of this sort are called paraconsistent. One of the oldest and best known approaches to the problem of designing useful paraconsistent logics is da Costa’s appr ..."
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Cited by 24 (15 self)
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In order to handle inconsistent knowledge bases in a reasonable way, one needs a logic which allows nontrivial inconsistent theories. Logics of this sort are called paraconsistent. One of the oldest and best known approaches to the problem of designing useful paraconsistent logics is da Costa’s
JAŚKOWSKI’S CRITERION
"... Abstract. A survey is given of threevalued paraconsistent propositional logics connected with Jaśkowski’s criterion for constructing paraconsistent logics. Several problems are raised and four new matrix threevalued paraconsistent logics are suggested. From the paper of Jaśkowski [14, p. 145] we ..."
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Abstract. A survey is given of threevalued paraconsistent propositional logics connected with Jaśkowski’s criterion for constructing paraconsistent logics. Several problems are raised and four new matrix threevalued paraconsistent logics are suggested. From the paper of Jaśkowski [14, p. 145] we
R.: Algebraic valuations as behavioral logical matrices, in: WoLLIC 2009, Selected Papers
 of Lecture Notes in Artificial Intelligence
, 2009
"... Abstract. The newly developed behavioral approach to the algebraization of logics extends the applicability of the methods of algebraic logic to a wider range of logical systems, namely encompassing manysorted languages and nontruthfunctionality. However, where a logician adopting the traditional ..."
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Cited by 4 (4 self)
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as the natural generalization of logical matrices to the behavioral setting, by establishing a few simple but promising results. For illustration, we will use da Costa’s paraconsistent logic C1. Key words: algebraic logic, behavioral algebraization, logical matrix, valuation semantics. 1
Rough Sets and 3Valued Logics
, 2008
"... In the paper we explore the idea of describing Pawlak’s rough sets using threevalued logic, whereby the value t corresponds to the positive region of a set, the value f — to the negative region, and the undefined value u — to the border of the set. Due to the properties of the above regions in rou ..."
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Cited by 2 (0 self)
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in rough set theory, the semantics of the logic is described using a nondeterministic matrix (Nmatrix). With the strong semantics, where only the value t is treated as designated, the above logic is a “common denominator” for Kleene and Łukasiewicz 3valued logics, which represent its two different
An algebraic perspective on valuation semantics ∗
, 2008
"... The class of socalled nontruthfunctional logics constitutes a challenge to the usual algebraic based semantic tools, such as matrix semantics [̷LS58]. The problem with these logics is the existence of noncongruent connectives that are not always interpreted homomorphically in a given algebra. The ..."
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Cited by 1 (1 self)
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The class of socalled nontruthfunctional logics constitutes a challenge to the usual algebraic based semantic tools, such as matrix semantics [̷LS58]. The problem with these logics is the existence of noncongruent connectives that are not always interpreted homomorphically in a given algebra
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