Abs t rac t . The coincidence of the declarative and procedural interpretations of logic programs does not apply to Prolog programs, due to the depth-first left-to-right evaluation strategy of Prolog interpreters. We propose a new semantics for Prolog programs based on a new fourvalued logic. The semantics is based on a new concept of completion analogous to Clark's and it enjoys the nice prope...

A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are developed, the latter in terms of (strict) indexed symmetric monoidal categories with comprehension. Various optional type formers are treated in a modular way. In ...

We present a higher-order inference system based on a formal compositional semantics and the wide-coverage CCG parser. We develop an improved method to bridge between the parser and semantic composition. The system is evaluated on the FraCaS test suite. In contrast to the widely held view that higher-order logic is unsuitable for efficient logical inferences, the results show that a system base...

The coincidence of the declarative and procedural interpretations of logic programs does not apply to Prolog programs, due to the depth-rst left-to-right evaluation strategy of Prolog interpreters. We propose a semantics for Prolog programs based on a four-valued logic. The semantics is based on a new concept of completion analogous to Clark's and it enjoys the nice properties of the declarativ...

We describe the operational semantics of the language for modelling logical concurrent systems (LCS). Such systems are characterised by atomic synchronous uniication. The model permits the description of both dependant and independent simultaneous actions or sets of atomic events. A semantics is given via labelled transition systems. The notion of equivalence over such systems is deened by stro...

We propose a solution to a long-standing problem in the foundations of well-founded semantics (WFS) for logic programs. The problem addressed is this: which (non-modal) logic can be considered adequate for well-founded semantics in the sense that its minimal models (appropriately defined) coincide with the partial stable models of a logic program? We approach this problem by identifying the HT ...

Dependency-based Compositional Semantics (DCS) is a framework of natural language semantics with easy-to-process structures as well as strict semantics. In this paper, we equip the DCS framework with logical inference, by defining abstract denotations as an abstraction of the computing process of denotations in original DCS. An inference engine is built to achieve inference on abstract denotati...

In this paper we develop a semantics of our approach based on commitments and arguments for conversational agents. We propose a logical model based on CTL* (Extended Computation Tree Logic) and on dynamic logic. Called Commitment and Argument Network (CAN), our formal framework based on this hybrid approach uses three basic elements: social commitments, actions that agents apply to these commit...

Unification-based grammar formalisms use structures containing sets of features to describe linguistic objects. Although computational algorithms for unification of feature structures have been worked out in experimental research, these algcwithms become quite complicated, and a more precise description of feature structures is desirable. We have developed a model in which descriptions of featu...

We construct a model for FPC, a purely functional, sequential, call-by-value language. The model is built from partial continuous functions, in the style of Plotkin, further constrained to be uniform with respect to a class of logical relations. We prove that the model is fully abstract.