Abduction in Logic Programming started in the late 80s, early 90s, in an attempt to extend logic programming into a framework suitable for a variety of problems in Artificial Intelligence and other areas of Computer Science. This paper aims to chart out the main developments of the field over the last ten years and to take a critical view of these developments from several perspectives: logical, epistemological, computational and suitability to application. The paper attempts to expose some of the challenges and prospects for the further development of the field.

In this paper, we review recent work aimed at the application of declarative logic programming to knowledge representation in artificial intelligence. We consider exten- sions of the language of definite logic programs by classical (strong) negation, disjunc- tion, and some modal operators and show how each of the added features extends the representational power of the language.

This paper introduces a variant of clausal normal form tableaux that we call "hyper tableaux". Hyper tableaux keep many desirable features of analytic tableaux while taking advantage of the central idea from (positive) hyper resolution, namely to resolve away all negative literals of a clause in a single inference step. Another feature of the proposed calculus is the extensive use of universally quantified variables. This enables new efficient forward-chaining proof procedures for full first order theories as variants of tableaux calculi.

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this paper, we generalize the program transformation techniques of [17] for non-abductive programs to deal with abductive frameworks. We introduce a new translation from an abductive logic program into a positive disjunctive program, and show that the belief models of an abductive program can be characterized by the fixpoint closure of the transformed disjunctive program. In the transformation, both negative hypotheses through negation as failure and positive hypotheses from the abducibles are dealt with uniformly. This fixpoint characterization is further extended to a fixpoint semantics for abductive extended disjunctive programs, i.e., abductive programs that permit classical negation as well as disjunctions. For a procedural aspect of our fixpoint semantics, we also show that a model generation procedure for positive disjunctive programs can be used as a sound and complete procedure for computing belief models for function-free and range-restricted programs.

We introduce a relevancy detection algorithm to be used in conjunction with the SATCHMO prover. The version of SATCHMO considered here is essentially a bidirectional prover, utilizing Prolog (back-chaining) on Horn clauses and forward-chaining on non-Horn clauses. Our extension, SATCHMORE (SATCHMO with RElevancy), addresses the major weakness of SATCHMO: the uncontrolled use of forward-chaining. By marking potentially relevant clause head literals, and then requiring that all the head literals be marked relevant (be "totally relevant") before a clause is used for forward-chaining, SATCHMORE is able to guide the use of these rules. Furthermore, the relevancy testing is performed without extending the proof search beyond what is done in SATCHMO. A simple implementation of the extended SATCHMO can be written in Prolog. We describe our relevancy testing approach, present the implementation, prove soundness and completeness, and provide examples which demonstrate the power of re...

A new fixpoint semantics for abductive logic programs is provided, in which the generalized stable models of an abductive program are characterized as the fixpoint of a disjunctive program obtained by a suitable program transformation. In the transformation, both negative hypotheses through negation as failure and positive hypotheses from the abducibles are dealt with uniformly. This characterization allows us to have a parallel bottomup model generation procedure for computing abductive explanations from arbitrary (range-restricted and function-free) general, extended, and disjunctive programs with integrity constraints. 1 Introduction Abduction, an inference to explanation, has recently been recognized as a very important form of reasoning for logic programming as well as various AI problems. In [EK89, KM90, Gel90, Ino91], abduction is expressed as an extension of logic programming. Eshghi and Kowalski [EK89] give an abductive interpretation of negation as failure [Cla78] in the cl...

KeY is a tool that provides facilities for formal specification and verification of programs within a commercial platform for UML based software development. Using the KeY tool, formal methods and object-oriented development techniques are applied in an integrated manner. Formal specification is performed using the Object Constraint Language (OCL), which is part of the UML standard. KeY provides support for the authoring and formal analysis of OCL constraints. The target language of KeY based development is JAVA CARD, a proper subset of JAVA for smart card applications and embedded systems. KeY uses a dynamic logic for JAVA CARD to express proof obligations, and provides a state-of-the-art theorem prover for interactive and automated verification. Apart from its integration into UML based software development, a characteristic feature of KeY is that formal specification and verification can be introduced incrementally.

We present a collection of simple but powerful techniques for enhancing the efficiency of tableau-based model generators such as Satchmo. The central ideas are to compile a clausal first order theory into a procedural Prolog program and to avoid redundant work of a naive implementation. We have compared various combinations of our techniques among each other and with theorem provers based on various calculi, using the TPTP Problem Library as a benchmark. Our implementation has turned out to be the most efficient for range-restricted problems and for a class of problems we call "non-nesting".

The presented approach aims at identifying false conjectures about free data types. Given a specification and a conjecture, the method performs a search for a model of an according counter specification. The model search is tailor-made for the semantical setting of free data types, where the fixed domain allows to describe models just in terms of interpretations.