Monotone Logic Programming

We propose a notion of an abstract logic. Based on this notion, we define abstract logic programs to be sets of sentences of an abstract logic. When these abstract logics possess certain logical properties (some properties considered are compactness, finitariness, and monotone consequence relations) we show how to develop a fixed-point, model-state-theoretic and proof theoretic semantics for such programs. The work of Melvin Fitting on developing a generalized semantics for multivalued logic programming is extended here to arbitrary abstract logics. We present examples to show how our semantics is robust enough to be applicable to various non-classical logics like temporal logic and multivalued logics, as well as to extensions of classical logic programming such as disjunctive logic programming. We also show how some aspects of the declarative semantics of distributed logic programming, particularly work of Ramanujam, can be incorporated into our framework

Strong Completeness Results for Paraconsistent Logic Programming

In [6], we introduced a means of allowing logic programs to contain negations in both the head and the body of a clause. Such programs were called generally Horn programs (GHPs, for short). The model-theoretic semantics of GHPs were defined in terms of four-valued Belnap lattices [5]. For a class of programs called well-behaved programs, an SLD-resolution like proof procedure was introduced. This procedure was proven (under certain restrictions) to be sound (for existential queries) and complete (for ground queries). In this paper, we remove the restriction that programs be well-behaved and extend our soundness and completeness results to apply to arbitrary existential queries and to arbitrary GHPs. This is the strongest possible completeness result for GHPs. The results reported here apply to the design of very large knowledge bases and in processing queries to knowledge bases that possibly contain erroneous information

Non-clausal multi-ary alpha-generalized resolution calculus for a finite lattice-valued logic

Due to the need of the logical foundation for uncertain information processing, development of efficient automated reasoning system based on non-classical logics is always an active research area. The present paper focuses on the resolution-based automated reasoning theory in a many-valued logic with truth-values defined in a lattice-ordered many-valued algebraic structure - lattice implication algebras (LIA). Specifically, as a continuation and extension of the established work on binary resolution at a certain truth-value level α (called α-resolution), a non-clausal multi-ary α-generalized resolution calculus is introduced for a lattice-valued propositional logic LP(X) based on LIA, which is essentially a non-clausal generalized resolution avoiding reduction to normal clausal form. The new resolution calculus in LP(X) is then proved to be sound and complete. The concepts and theoretical results are further extended and established in the corresponding lattice-valued first-order logic LF(X) based on LIA

Amalgamating Knowledge Bases, III - Algorithms, Data Structures, and Query Processing

Integrating knowledge from multiple sources is an important aspect of automated reasoning systems. In the first part of this series of papers, we presented a uniform declarative framework, based on annotated logics, for amalgamating multiple knowledge bases when these knowledge bases (possibly) contain inconsistencies, uncertainties, and non-monotonic modes of negation. We showed that annotated logics may be used, with some modifications, to mediate between different knowledge bases. The multiple knowledge bases are amalgamated by embedding the individual knowledge bases into a lattice. In this paper, we briefly describe an SLD-resolution based proof procedure that is sound and complete w.r.t. our declarative semantics. We will then develop an OLDT -resolution based query processing procedure, MULTI-OLDT , that satisfies two important properties: (1) efficient reuse of previous computations is achieved by maintaining a table -- we describe the structure of this table and show that table operations can be efficiently executed, and (2) approximate, interruptable query answering is achieved, i.e. it is possible to obtain an ``intermediate, approximate'' answer from the query processing procedure by interrupting it at any point in time during its execution. The design of the MULTI-OLDT procedure will include the development of run-time algorithms to incrementally and efficiently update the table. (Also cross-referenced as UMIACS-TR-94-35

Foundations of Fuzzy Logic and Semantic Web Languages

This book is the first to combine coverage of fuzzy logic and Semantic Web languages. It provides in-depth insight into fuzzy Semantic Web languages for non-fuzzy set theory and fuzzy logic experts. It also helps researchers of non-Semantic Web languages get a better understanding of the theoretical fundamentals of Semantic Web languages. The first part of the book covers all the theoretical and logical aspects of classical (two-valued) Semantic Web languages. The second part explains how to generalize these languages to cope with fuzzy set theory and fuzzy logic

Foundations of Fuzzy Logic and Semantic Web Languages

This book is the first to combine coverage of fuzzy logic and Semantic Web languages. It provides in-depth insight into fuzzy Semantic Web languages for non-fuzzy set theory and fuzzy logic experts. It also helps researchers of non-Semantic Web languages get a better understanding of the theoretical fundamentals of Semantic Web languages. The first part of the book covers all the theoretical and logical aspects of classical (two-valued) Semantic Web languages. The second part explains how to generalize these languages to cope with fuzzy set theory and fuzzy logic

Logic programs with uncertainty: neural computations and automated reasoning

Abstract. Bilattice-based annotated logic programs (BAPs) form a very general class of programs which can handle uncertainty and conflicting information. We use BAPs to integrate two alternative paradigms of computation: specifically, we build learning artificial neural networks which can model iterations of the semantic operator associated with each BAP and introduce sound and complete SLD-resolution for this class of programs. Key words: Logic programs, artificial neural networks, SLD-resolution

Sound and complete SLD-resolution for bilattice-based annotated logic programs

We introduce the class of normal bilattice-based annotated first-order logic programs (BAPs) and develop declarative and operational semantics for them. In particular, SLD-resolution for these programs is defined and its soundness and completeness established

Proceedings of the 11th Workshop on Nonmonotonic Reasoning

These are the proceedings of the 11th Nonmonotonic Reasoning Workshop. The aim of this series is to bring together active researchers in the broad area of nonmonotonic reasoning, including belief revision, reasoning about actions, planning, logic programming, argumentation, causality, probabilistic and possibilistic approaches to KR, and other related topics. As part of the program of the 11th workshop, we have assessed the status of the field and discussed issues such as: Significant recent achievements in the theory and automation of NMR; Critical short and long term goals for NMR; Emerging new research directions in NMR; Practical applications of NMR; Significance of NMR to knowledge representation and AI in general