Hybrid Rules with Well-Founded Semantics

A general framework is proposed for integration of rules and external first order theories. It is based on the well-founded semantics of normal logic programs and inspired by ideas of Constraint Logic Programming (CLP) and constructive negation for logic programs. Hybrid rules are normal clauses extended with constraints in the bodies; constraints are certain formulae in the language of the external theory. A hybrid program is a pair of a set of hybrid rules and an external theory. Instances of the framework are obtained by specifying the class of external theories, and the class of constraints. An example instance is integration of (non-disjunctive) Datalog with ontologies formalized as description logics. The paper defines a declarative semantics of hybrid programs and a goal-driven formal operational semantics. The latter can be seen as a generalization of SLS-resolution. It provides a basis for hybrid implementations combining Prolog with constraint solvers. Soundness of the operational semantics is proven. Sufficient conditions for decidability of the declarative semantics, and for completeness of the operational semantics are given

LUPS - A language for updating logic programs

Most of the work conducted so far in the field of logic programming has focused on representing static knowledge, i.e. knowledge that does not evolve with time. To overcome this limitation, in a recent paper, the authors introduced the concept of dynamic logic programming. There, they studied and defined the declarative and operational semantics of sequences of logic programs (or dynamic logic programs), P-o + ... + P-n. Each such program contains knowledge about some given state, where different states may, e.g., represent different time periods or different sets of priorities. The role of dynamic logic programming is to employ relationships existing between the possibly mutually contradictory sequence of programs to precisely determine, at any given state, the declarative and procedural semantics of their combination. But how, in concrete situations, is a sequence of logic programs built? For instance, in the domain of actions, what are the appropriate sequences of programs that represent the performed actions and their effects? Whereas dynamic logic programming provides a way for determining what should follow, given the sequence of programs, it does not provide a good practical language for the specification of updates or changes in the knowledge represented by successive logic progams. In this paper we define a language designed for specifying changes to logic programs (LUPS - "Language for dynamic updates"). Given an initial knowledge base (in the form of a logic program) LUPS provides a way for sequentially updating it. The declarative meaning of a sequence of sets of update actions in LUPS is defined using the semantics of the dynamic logic program generated by those actions. We also provide a translation of the sequence of update statements sets into a single generalized logic program written in a meta-language, so that the stable models of the resulting program correspond to the previously defined declarative semantics. This meta-language is used in the actual implementation, although this is not the subject of this paper. Finally we briefly mention related work (lack of space prevents us from presenting more detailed comparisons).publishe

A Survey of Paraconsistent Semantics for Logic Programs

In this chapter we motivate the use of paraconsistency, and survey the most salient paraconsistent semantics for (extended) logic programs, which are briefly defined and explained. Most of the semantics are accompanied with their multi-valued model theory, giving them a new perspective. The survey also presents new results regarding the embedding of part of these semantics into normal logic programs under Well-Founded Semantics [20], Partial Stable Model Semantics (or stationary semantics) [48], and Stable Model Semantics [21]. Furthermore, a concise recapitulation of other related paraconsistent formalisms is made. The reader is assumed to have a good knowledge of the semantics of normal logic programs. We believe a comprehensive coverage of the topic as it stands at present is attained here

Non-Monotonic Reasoning Based on Minimal Models and its Efficient Implementation

. A common approach to non--monotonic reasoning is to choose a set S of models (e.g. minimal, perfect or stable models) for a logic program P . Then, the meaning of P is defined as the set of all formulas which are implied logically by all models in S. For a disjunctive logic program P , we consider the set S = MMP of minimal models and get the non--montonic consequences NMP of ground disjunctions over positive or negative literals. The set NMP consists of three subsets: The minimal model state MSP (ground disjunctions over positive literals), the negated extended generalized closed world assumption :EGCWA P (ground disjunctions over negative literals), and the rest (mixed disjunctions over positive and negative literals). We show that the mixed disjunctions are implied logically by MSP [:EGCWA P . Thus the interesting sets are the logical consequences MSP and the non-- monotonic consequences :EGCWA P . As described in [16], MSP consists of the positive ground disjunctions, which ar..

Inductive Theorem Proving by Consistency for First-Order Clauses

. We show how the method of proof by consistency can be extended to proving properties of the perfect model of a set of first-order clauses with equality. Technically proofs by consistency will be similar to proofs by case analysis over the term structure. As our method also allows to prove sufficient-completeness of function definitions in parallel with proving an inductive theorem we need not distinguish between constructors and defined functions. Our method is linear and refutationally complete with respect to the perfect model, it supports lemmas in a natural way, and it provides for powerful simplification and elimination techniques. 1 Introduction For proving inductive theorems of equational theories "proof by consistency" is a particularly powerful method. The method has been engineered during the last decade by gradually removing restrictions on the specification side, by reducing the search space for inferences, and by including methods from term rewriting for the simplificat..

Nonmonotonic Reasoning In LDL++

Deductive database systems have made major advances on efficient support for nonmonotonic reasoning. A first generation of deductive database systems supported the notion of stratification for programs with negation and set aggregates. Stratification is simple to understand and efficient to implement but it is too restrictive; therefore, a second generation of systems seeks efficient support for more powerful semantics based on notions such as well-founded models and stable models. In this respect, a particularly powerful set of constructs is provided by the recently enhanced LDL++ system that supports (i) monotonic user-defined aggregates, (ii) XY-stratified programs, and (iii) the nondeterministic choice constructs under stable model semantics. This integrated set of primitives supports a terse formulation and efficient implementation for complex computations, such as greedy algorithms and data mining functions, yielding levels of expressive power unmatched by other deductive..