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9th International Workshop on Multi-Disciplinary Trends in Artificial Intelligence (MIWAI)

作者： Jayakumar, Badrinath Sunderraman, Rajshekhar Georgia State Univ Dept Comp Sci Atlanta GA 30303 USA

ISBN: (纸本)9783319261812;9783319261805

Positive extended disjunctive deductive databases are those that contain explicit negation both in the head and body of the clauses. For such databases, paraconsistent minimal models (p-minimal models) have been proposed based on multi-valued logic (four-valued logic). Moreover, the paraconsistent relational model is also based on four-valued logic. In this paper, we propose an algorithm, which converts clauses to equations and solves it, to find p-minimal models using the paraconsistent relational model. In order to accomplish that, we use disjunctive paraconsistent relation model.

关键词： Inconsistency paraconsistent relational model Fixed-point semantics Four-valued logic

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Description Logic Programs: A paraconsistent relational model Approach 14th

Description Logic Programs: A Paraconsistent Relational Mode...

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14th Mexican International Conference on Artificial Intelligence (MICAI)

作者： Jayakumar, Badrinath Sunderraman, Rajshekhar Georgia State Univ Dept Comp Sci Atlanta GA 30303 USA

ISBN: (纸本)9783319270609;9783319270593

A description logic program (dl-program) consists of a description logic knowledge base (a terminological box and an assertion box) and a set of rules for a logic program. For such description logic programs, instead of providing the fixed-point semantics for dl-programs by the immediate consequence operator, we propose an algorithm based on the paraconsistent relational model that mimics the immediate consequence operator of dl-programs. We also introduce a dl-paraconsistent relation (dl-relation), which is essential for sending information between description logic and logic programs represented in terms of equations containing paraconsistent relations. The first step in our algorithm is to convert rules, which may contain dl-atoms that enable the flow of information between description logic and logic programs, into paraconsistent relation equations that contain paraconsistent relational algebraic operators. The second step is to determine iteratively the fixed-point semantics for dl-programs using these equations. We will also prove the correctness of both steps of the algorithm.

关键词： Description logic Logic programs Fixed-point semantics paraconsistent relational model

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Quasi-classical reasoning in paraconsistent databases

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ANNALS OF MATHEMATICS AND ARTIFICIAL INTELLIGENCE 2018年第1-3期82卷 131-159页

作者： Jayakumar, Badrinath Sunderraman, Rajshekhar Georgia State Univ Atlanta GA 30303 USA

The well-founded model for any general deductive database computed using the paraconsistent relational model, based on four-valued logic, does not support inference rules such as disjunctive syllogism. In order to support disjunctive syllogism, we utilize the generalization of the relational model to quasi-classic (QC) logic, whose inference power is much closer to classical logic. As the paraconsistent relational model is capable of representing incomplete and inconsistent data, we propose an algorithm to find QC model for inconsistent positive extended disjunctive deductive databases. We also provide the proof for the algorithm.

关键词： Quasi-classical logic paraconsistent relational model Fixpoint semantics Inconsistency

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