Mehmet A. Orgun

An Overview of Temporal and Modal Logic Programming

This paper presents an overview of the development of the field of temporal and modal logic programming. We review temporal and modal logic programming languages under three headings: (1) languages based on interval logic, (2) languages based on temporal logic, and (3) languages based on (multi)modal logics. The overview includes most of the major results developed, and points out some of the similarities, and the differences, between languages and systems based on diverse temporal and modal logics. The paper concludes with a brief summary and discussion.

Dealing with multiple granularity of time in temporal logic programming

Abstract Chronolog(MC) is an extension of logic programming based on a linear-time temporal logic with multiple granularity of time called TLC . A Chronolog(MC) program consists of a clock definition, a clock assignment and a program body. Each predicate symbol appearing in the program body is associated with a local clock through the clock definition and assignment. This paper investigates the logical basis of the language, presents a clocked temporal resolution where time-matching is essential, and in particular proposes three algorithms for time-matching. The paper also discusses the declarative semantics of Chronolog(MC) programs in terms of clocked temporal Herbrand models. It is shown that Chronolog(MC) programs also satisfy the minimum model semantics. The language can be used to model a wide range of simulation systems and other relevant tasks where the notion of dynamic change is central.

ON TEMPORAL DEDUCTIVE DATABASES

This article introduces a temporal deductive database system featuring a logic programming language and an algebraic front‐end. The language, called Temporal DATALOG, is an extension of DATALOG based on a linear‐time temporal logic in which the flow of time is modeled by the set of natural numbers. Programs of Temporal DATALOG are considered as temporal deductive databases, specifying temporal relationships among data and providing base relations to the algebraic front‐end. The minimum model of a given Temporal DATALOG program is regarded as the temporal database the program models intensionally. The algebraic front‐end, called TRA, is a point‐wise extension of the relational algebra upon the set of natural numbers. When needed during the evaluation of TRA expressions, slices of temporal relations over intervals can be retrieved from a given temporal deductive database by bottom‐up evaluation strategies.

Multi-dimensional logic programming: theoretical foundations

Abstract This paper introduces an extension of logic programming based on multi-dimensional logics, called MLP. In a multi-dimensional logic the values of elements vary depending on more than one dimension, such as time and space. The resulting logic programming language is suitable for modelling objects which involve implicit and/or explicit temporal and spatial dependencies. The execution of programs of the language is based on a resolution-type proof procedure called MSLD-resolution (for multi-dimensional SLD-resolution). The paper also establishes the declarative semantics of multi-dimensional logic programs, based on an extension of Herbrand models. In particular, it is shown that MLP programs satisfy the minimum model semantics. A novel multidimensional interface to MLP is also outlined; it can be used as a powerful development tool with the advantage of non-determinism inherent in logic programming.

Extending Temporal Logic Programming with Choice Predicates Non-determinism

In temporal logic programming, a stream can be specified by a single-valued, time-varying predicate which, at any given moment in time, represents the corresponding element in the stream. However, due to inherent nondeterminism in logic programming, time-varying predicates do not necessarily represent single-valued relations at any given moment in time. Choice predicates are also time-varying predicates, but, in principle, they act like a dataflow node with multiple input lines which nondeterministically selects one of its inputs as output. Therefore they are guaranteed to be single-valued at all moments in time, and they can be regarded as representing “nondeterministic” streams. Users do not define choice predicates, they are supplied automatically for all predicates defined in temporal logic programs. Inputs to choice predicates are supplied by the corresponding predicates. When the connection between choice predicates and the corresponding predicates is established, we obtain non-Horn temporal logic programs as a result. The model-theoretic semantics of such a program is developed in terms of “minimal models”. However, the logical structure of the program dictates which minimal models are constructible from the program. We in particular discuss a characterization of constructible minimal models as limits of chains of models obtained by alternating applications of two new mappings NTP and CP . The paper also outlines a proof procedure for the temporal language Chronolog extended with choice predicates.

Chronolog(Z): linear-time logic programming

This paper introduces Chronolog(Z), a logic programming language based on a discrete linear-time temporal logic with unbounded past and future. Chronolog(Z) is suitable for applications involving the notion of dynamic change such as modeling non-terminating computations, the simulation of sequential circuits, and temporal databases. The execution of the programs of the language is based on a resolution-type proof procedure called TiSLD-resolution. A modular extension of Chronolog(Z) is proposed which can be used to model objects with internal memory.<<ETX>>

An abstract execution model for temporal logic programs

The paper proposes an abstract execution model which can be used as the basis for implementing temporal logic programs on multi-processor architectures. Temporal logic programs offer a form of parallelism, which we call temporal-parallelism, that does not exist in standard logic programs. Temporal-parallelism means that computations at different moments in time can be performed in parallel and independently of each other. We also outline the mapping of the abstract model onto a network of processors.<<ETX>>