Comparative metric semantics for concurrent Prolog

AbstractThis paper shows the equivalence of two semantics for a version of Concurrent Prolog with non-flat guards: an operational semantics based on a transition system and a denotational semantics which is a metric semantics (the domains are metric spaces). We do this in the following manner. First a uniform language L is considered, that is a language where the atomic actions have arbitrary interpretations. For this language we define an operational and a denotational semantics, and we prove that the denotational semantics is correct with respect to the operational semantics. This result relies on Banach's fixed point theorem. Techniques stemming from imperative languages are used. Then we show how to translate a Concurrent Prolog program to a program in L by selecting certain basic sets for L and then instantiating the interpretation function for the atomic actions. In this way we induce the two semantics for Concurrent Prolog and the equivalence between the two semantics

Semantic models for concurrent logic languages

AbstractIn this paper we develop semantic models for a class of concurrent logic languages. We give two operational semantics based on a transition system, a declarative semantics and a denotational semantics. One operational and the declarative semantics model the success set, that is, the set of computed answer substitutions corresponding to all successfully terminating computations. The other operational and the denotational semantics also model deadlock and infinite computations. For the declarative and the denotational semantics we extend standard notions such as unification in order to cope with the synchronization mechanism of the class of languages we study. The basic mathematical structure for the declarative semantics is the complete lattice of sets of finite streams of substitutions. In the denotational semantics, we use a complete metric space of tree-like structures that are labelled with functions that represent the basic unification step. We look at the relations between the different models. We relate first the two operational semantics and next the declarative and denotational semantics with their respective operational counterparts

The Role of Deontic Logic in the Specification of Information Systems

In this paper we discuss the role that deontic logic plays in the specification of information systems, either because constraints on the systems directly concern norms or, and even more importantly, system constraints are considered ideal but violable (so-called `soft¿ constraints).\ud To overcome the traditional problems with deontic logic (the so-called paradoxes), we first state the importance of distinguishing between ought-to-be and ought-to-do constraints and next focus on the most severe paradox, the so-called Chisholm paradox, involving contrary-to-duty norms. We present a multi-modal extension of standard deontic logic (SDL) to represent the ought-to-be version of the Chisholm set properly. For the ought-to-do variant we employ a reduction to dynamic logic, and show how the Chisholm set can be treated adequately in this setting. Finally we discuss a way of integrating both ought-to-be and ought-to-do reasoning, enabling one to draw conclusions from ought-to-be constraints to ought-to-do ones, and show by an example the use(fulness) of this