José Luis Carballido

Logical Weak Completions of Paraconsistent Logics

Let P be an arbitrary theory and let X be any given logic. Let M be a set of atoms. We say that M is a X-stable model of P if M is a classical model of P and P∪¬M~ proves in logic X all atoms in M, this is denoted by P∪¬M~ ⊩xM. We prove that being an X-stable model is an invariant property for disjunctive programmes under a large class of logics. Two kinds of logics are mainly considered: paraconsistent logics and normal modal logics. For modal logics we use a translation proposed by Gelfond that replaces ¬a with ¬□a. As a consequence we prove that several semantics (recently introduced) for non-monotonic reasoning are equivalent for disjunctive programmes. In addition, we show that such semantics can be characterized by a fixed-point operator in terms of classical logic. We also present a simple translation of a disjunctive programme D into a normal programme N, such that the PStable model semantics of N corresponds to the stable semantics of D over the common language. We present the formal proof of this statement.

Equivalence for the G 3 ′ -stable models semantics

Abstract We study the notion of strong equivalence between two disjunctive logic programs under the G 3 ′ -stable model semantics, also called the p-stable semantics, and we show how some particular cases of testing strong equivalence between programs can be reduced to checking whether a formula is a theorem in some paraconsistent logic, or in some cases in classical logic. We also present some program transformations for disjunctive programs which can be used to reduce the size of a program.

Yet another application of fuzzy logic

Fuzzy logic has been mainly used for fuzzy control and other applications. Recently, it also has been studied as a symbolic logic with syntax and semantics. We know that fuzzy logic is a branch of many-valued logic based on the paradigm of inference under vagueness. In this paper, we consider a particular many valued logic to show a non-standard application of fuzzy logic. We propose to use it for knowledge representation based on logic programming.

Defining Stage Argumentation Semantics in Terms of an Abducible Semantics

We define a new logic programming semantics in terms of abducible atoms. We use it to characterize the stage extensions of an argumentation framework AF by means of an associated normal program PAF. We also define the stage semantics for a special type of normal programs and present a similar characterization.

An application of clasp in the study of logics

We show how to use the Answer Set Programming (ASP) tool called clasp to prove that there exists a unique three-valued paraconsistent logic that satisfies the substitution property and is sound with respect to da Costa Cω logic.

Updates Based on ASP

We present a semantics for an update operator. This semantics is based on a concept called minimal generalized answer sets.

P-stable models of strong kernel programs

The research community has long recognized the study of non-monotonic reasoning (NMR) as a promising approach to model features of commonsense reasoning. We study one of the semantics that are useful to formalize NMR, called the p-stable semantics. We introduce three different formats for normal programs: negative normal programs, restricted negative normal programs and strong kernel programs. These forms help to simplify the search of p-stable models of the original program. One of the main results of this paper indicates that the p-stable semantics for strong kernel programs is the same as the stable semantics. This way, all the applications based on stable semantics for those kernel programs (defined in [S. Costantini, A. Provetti, Normal forms for answer set programming, J. Theory Pract. Log. Program. 5 (2005) 747-760]) that are strong kernel programs can also be based on the p-stable semantics.

Computing of p-Stable Models Based on Semi-Negative Normal Programs with Constraints

Currently non-monotonic reasoning (NMR) is a promising approach to model features of common sense reasoning. In order to formalize NMR the research community has applied monotonic logics. The present paper furthers the study of one of the semantics useful in this formalization called p-stable. We introduce three different formats for normal programs with constraints: negative normal programs, restricted negative normal programs and semi-negative normal programs. These forms help to simplify the search of p-stable models of the original program. One of the main results of this paper indicates that the p-stable semantics for semi-negative normal programs with constraints agrees with the Comp semantics. In this way all the applications based on the Comp semantics of semi-negative programs can also be based on p-stable semantics of this type of programs. It is worth to mention that this class of programs can express interesting problems as the 3-coloring problem.

On Paraconsistent Extensions of C1

We show that logic C1 cannot be extended to a paraconsistent logic in which the substitution theorem is valid. We show that C1 can be extended to larger paraconsistent logics by adding some desirable properties as axioms. We use three-valued logics to support our claims.

Preferences for Argumentation Semantics

We propose an engineering approach for assembling argumentation theory with a preference approach, which allows us to give as input an argumentation problem with preferences and return the stable argumentation extensions that fulfill the preferences.