Tim: The toulouse inference machine for non-classical logic programming

Abstract

We present an environment for logic programming languages called Toulouse Inference Machine (TIM). Its meta-level architecture permits the user to define how to compute a new goal from a given one. Our aim is to define a frame as general as possible for creating extensions of Prolog and, in particular, to provide a general methodology to implement non-classical logics. There are three basic assumptions on which our frame is built: first, to keep as a base the fundamental logic programming mechanisms that are backward chaining, depth first strategy, backtracking, and unification; second, to parametrize the inference step, and finally, to select clauses "by hand". Applications in logic programming and, in particular, in non-classic logic programming are presented: we specify with a few TIM inference rules various extensions of Prolog by non-classical concepts which have been proposed in the literature.

4 Computational modal logic

“…Following the direct approach, [21,20] presents a declarative semantics and an SLD resolution calculus for a class of modal logic programs in modal logics KD, KT, and S4, while [22,23] present a framework for developing the fixpoint and operational semantics of a class of multimodal logic programs where additional properties of modal operators can be described by axiom schemas of the form [142] presenting a fixpoint semantics, least model semantics, and an SLD resolution calculus for modal logic programs in modal logics extending K with a non-empty selection of the axiom schemas B, D, T, 4 and 5. Also, modal logic programs in [142] are as expressive as the general modal Horn fragment which allows arbitrary occurrences of the modal operators 2 and 3 in programs clauses and goals.…”

“…Implementations of systems based on the direct approach include MOLOG [62,63], MProlog [141,143], and TIM [21]. However, just as for the direct resolution approaches described in Section 5.2, little work seems to have been conducted on developing specialised and efficient data structures and algorithms for such systems, with the exception of [2] which describes an abstract machine model for MOLOG, in analogue to the Warren Abstract Machine model for Prolog [191].…”

A modal extension of logic programming: modularity, beliefs and hypothetical reasoning

“…( To show that c knows that he has got a white spot, let us assume c knows that he has got a black spot and let us prove a contradiction: Note that we have modeled only one situation here. In order to generalize the problem we can remove clauses (4) and 5 In this section we have de ned a goal directed proof procedure for a speci c modal language with a collection of modalities of type K and a modality of type S4. In this procedure the properties of modalities are taken into account in the de nition of the matching relation.…”

An introduction to executable temporal logics

“…This involves defining the particular algebra s4, providing a translation from Temporal Horn Clauses, and TEMPLOG clauses in particular, to elements of si, and establishing that TSLD-resolution is a (restricted) form of the CLP-derivation mechanism over si. • Balbiani et al (1991) describe the Toulouse Inference Machine (TIM), which provides a metalanguage for defining extensions of logic programming based upon non-classical logics. The basic idea is to add the notion of contexts to standard logic programming and allow meta-rules to manipulate these.…”