of all possible paraconsistent determinizations of a nondeterministic matrix, thus representing what is really essential for their maximal paraconsistency.

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 5-valued characteristic nondeterministic matrix for mCi. This provides a quite non-trivial example for the utility and effectiveness of the use

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

inconsistent, conicting or contradictory information. Like many paraconsistent logics they are non-structural, 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

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

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

Abstract. A survey is given of three-valued paraconsistent propositional logics connected with Jaśkowski’s criterion for constructing paraconsistent logics. Several problems are raised and four new matrix three-valued para-consistent logics are suggested. From the paper of Jaśkowski [14, p. 145] we

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

in rough set theory, the semantics of the logic is described using a non-deterministic 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 3-valued logics, which represent its two different

The class of so-called non-truth-functional 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