Luke Simon

Abstract. Real world applications of action description languages involve systems that have real-time constraints. The occurrence of an action is just as important as the time at which the action occurs. In order to be able to model such real-time systems, the action description language A is extended with real-time clocks and constraints. The formal syntax and semantics of the extended language are defined, and the use of logic programming as a means to an implementation of real-time A is discussed.

To fully utilize Web-services, users and applications should be able to discover, deploy, compose and synthesize services automatically. This automation can take place only if a formal semantic description of the Web-services is available. In this paper we present the design of USDL (Universal Service Description Language), a language for formally describing the semantics of information utilized and produced by Web-services. USDL is based on the Web ontology language (OWL) and employs WordNet as a common basis for understanding the meaning of services. USDL can be regarded as formal program documentation that will allow sophisticated conceptual modeling and searching of available Web-services, automated service composition, and other forms of automated service integration. The preliminary design of USDL is presented, along with examples, and its formal semantics given.

Abstract Traditional logic programming, with its minimal Herbrand model semantics, is useful for declaratively defining finite data structures and properties. A program in traditional logic programming defines a set of inference rules that can be used to automatically construct proofs of various logical statements. The fact that logic programming also has a goal directed, top-down operational semantics, means that these proofs can efficiently be constructed by" executing" the logical statement that is to be proved. However, since ...

Coinduction has recently been introduced as a powerful technique for reasoning about unfounded sets, unbounded structures, and interactive computations. Where induction corresponds to least fixed point semantics, coinduction corresponds to greatest fixed point semantics. In this paper we discuss the introduction of coinduction into logic programming. We discuss applications of coinductive logic programming to verification and model checking, lazy evaluation, concurrent logic programming and non-monotonic reasoning.

We extend logic programming’s semantics with the semantic dual of traditional Herbrand semantics by using greatest fixed-points in place of least fixed-points. Executing a logic program then involves using coinduction to check inclusion in the greatest fixed-point. The resulting coinductive logic programming language is syntactically identical to, yet semantically subsumes logic programming with rational terms and lazy evaluation. We present a novel formal operational semantics that is based on synthesizing a coinductive hypothesis for this coinductive logic programming language. We prove that this new operational semantics is equivalent to the declarative semantics. Our operational semantics lends itself to an elegant and efficient goal directed proof search in the presence of rational terms and proofs. We describe a prototype implementation of this operational semantics along with applications of coinductive logic programming.