The Legal Knowledge Engineering is a new topic of investigationof Artificial Intelligence. This paper discusses some relevant problems relatedto this new area in a summarized way. Within the Normative Law Theory,one question that arises naturally is that of contradiction, like for example:articles conflicting with other articles inside the same code, codes conflictingwith codes, codes conflicting with jurisprudence, and in general, treatmentswith conflicting propositions in Normative Law Theory. This paper suggeststo treat directly inconsistencies in the Legal Knowledge Engineering; thisengineering has as (...) underlying logic a paraconsistent annotated deontic logic.There are three main approximations in Legal Knowledge Engineering basedon: cases, rules and logic. In this paper, we consider the approximationbased on logic. It is considered a paraconsistent annotated deontic logic.Based on this logic, it is established a new proposal that is called Paraconsistent Legal Knowledge Engineering. For this proposal, it it is suggested ameta-interpreter to support the deontic operators as well as inconsistency —entitled on this paper Paralog D that can be used as a base to handle withthe issues discussed. (shrink)

In this paper we present an overview of Professor Newton C. A. da Costa’s work in logic, emphasizing the main results obtained by him in the several areas of his research activity. The text furnish a detailed bibliographic reference of his works, which are listed in the last section.

Jaśkowski [3] presented a new propositional calculus labeled “discussive propositional calculus”, to serve as an underlying basis for inconsistent but non-trivial theories. This system was later extended to lower andhigher order predicate calculus . Jaśkowski’s system of discussiveor discursive propositional calculus can actually be extended to predicatecalculus in at least two ways. We have the intention using this calculus ofbuilding later as a basis for a discussive theory of sets. One way is thatstudied by Da Costa and Dubikajtis. Another one (...) is developed in this paperas a solution to a problem formulated by Da Costa. In this work we study afirst order discussive predicate calculus J∗∗.The paper consists of three parts. In the first part we introduce thecalculus J∗∗ and, following Prof. D. Makinson’s suggestion, we show that itis not identical with the predicate calculus [2] of Da Costa and Dubikajtis.An axiomatization of J∗∗ is presented. In the second one, we introduce newdiscussive connectives and study some of the properties. We observe thatthe usual Kripke semantics can be adapted to the calculus J∗∗. (shrink)