An Intelligent Backtracking Schema in a Logic Programming Environment

We present a new method to represent variable bindings in the Warren Abstract Machine (WAM), so that the ages of variable bindings can be easily found using this new representation in our intelligent backtracking schema. The age of a variable bound to a non-variable term is the youngest choice point such that backtracking to that choice point can make that variable an unbound variable again. The procedure backtracking point is the choice point of the procedure currently being executed or the choice point of its first ancestor having a choice point. Variable ages and procedure backtracking points are used in the process of figuring out backtracking points in our intelligent backtracking schema. Our intelligent backtracking schema performs much better than the results of other intelligent backtracking methods in the literature for deterministic programs, and its performance for non-deterministic programs are comparable with their results

Extending the Finite Domain Solver of GNU Prolog

International audienceThis paper describes three significant extensions for the Finite Domain solver of GNU Prolog. First, the solver now supports negative integers. Second, the solver detects and prevents integer overflows from occurring. Third, the internal representation of sparse domains has been redesigned to overcome its current limitations. The preliminary performance evaluation shows a limited slowdown factor with respect to the initial solver. This factor is widely counterbalanced by the new possibilities and the robustness of the solver. Furthermore these results are preliminary and we propose some directions to limit this overhead

Preprints of Proceedings of GWAI-92

This is a preprint of the proceedings of the German Workshop on Artificial Intelligence (GWAI) 1992. The final version will appear in the Lecture Notes in Artificial Intelligence

Goal driven theorem proving using conceptual graphs and Peirce logic

The thesis describes a rational reconstruction of Sowa's theory of Conceptual Graphs. The reconstruction produces a theory with a firmer logical foundation than was previously the case and which is suitable for computation whilst retaining the expressiveness of the original theory. Also, several areas of incompleteness are addressed. These mainly concern the scope of operations on conceptual graphs of different types but include extensions for logics of higher orders than first order. An important innovation is the placing of negation onto a sound representational basis. A comparison of theorem proving techniques is made from which the principles of theorem proving in Peirce logic are identified. As a result, a set of derived inference rules, suitable for a goal driven approach to theorem proving, is developed from Peirce's beta rules. These derived rules, the first of their kind for Peirce logic and conceptual graphs, allow the development of a novel theorem proving approach which has some similarities to a combined semantic tableau and resolution methodology. With this methodology it is shown that a logically complete yet tractable system is possible. An important result is the identification of domain independent heuristics which follow directly from the methodology. In addition to the theorem prover, an efficient system for the detection of selectional constraint violations is developed. The proof techniques are used to build a working knowledge base system in Prolog which can accept arbitrary statements represented by conceptual graphs and test their semantic and logical consistency against a dynamic knowledge base. The same proof techniques are used to find solutions to arbitrary queries. Since the system is logically complete it can maintain the integrity of its knowledge base and answer queries in a fully automated manner. Thus the system is completely declarative and does not require any programming whatever by a user with the result that all interaction with a user is conversational. Finally, the system is compared with other theorem proving systems which are based upon Conceptual Graphs and conclusions about the effectiveness of the methodology are drawn

Combination of convex theories: Modularity, deduction completeness, and explanation

AbstractDecision procedures are key components of theorem provers and constraint satisfaction systems. Their modular combination is of prime interest for building efficient systems, but their effective use is often limited by poor interface capabilities, when such procedures only provide a simple “sat/unsat” answer. In this paper, we develop a framework to design cooperation schemas between such procedures while maintaining modularity of their interfaces. First, we use the framework to specify and prove the correctness of classic combination schemas by Nelson–Oppen and Shostak. Second, we introduce the concept of deduction complete satisfiability procedures, we show how to build them for large classes of theories, then we provide a schema to modularly combine them. Third, we consider the problem of modularly constructing explanations for combinations by re-using available proof-producing procedures for the component theories

Derivation of logic programs

Imperial Users onl