The Greatest Extension of S4 into which Intuitionistic Logic is Embeddable

This paper gives a characterization of those quasi-normal extensions of the modal system S4 into which intuitionistic propositional logic Int is embeddable by the Gödel translation. It is shown that, as in the normal case, the set of quasi-normal modal companions of Int contains the greatest logic, M*, for which, however, the analog of the Blok-Esakia theorem does not hold. M* is proved to be decidable and Halldén-complete; it has the disjunction property but does not have the finite model property.     

Curry's paradox in contractionless constructive logic

We propose contractionless constructive logic which is obtained from Nelson's constructive logic by deleting contractions. We discuss the consistency of a naive set theory based on the proposed logic in relation to Curry's paradox. The philosophical significance of contractionless constructive logic is also argued in comparison with Fitch's and Prawitz's systems.     

Deontic database constraints,violation and recovery

The paper discusses the potential value of a deontic approach to database specification. More specifically, some different types of integrity constraints are considered and a distinction is drawn between necessary (hard) and deontic (soft) constraints.Databases are compared with other normative systems. A deontic logic for database specification is proposed and the problems of how to react to, and of how to correct, or repair, a situation which arises through norm violation are discussed in the context of this logic. The limitations of the proposed logic and possible modifications and extensions of it are analysed.     

Axiomatising first-order temporal logic: Until and since over linear time

We present an axiomatisation for the first-order temporal logic with connectives Until and Since over the class of all linear flows of time. Completeness of the axiom system is proved.We also add a few axioms to find a sound and complete axiomatisation for the first order temporal logic of Until and Since over rational numbers time.The author would like to thank Dov Gabbay and Ian Hodkinson for helpful discussions on this material. The work was supported by the U.K. Science and Engineering Research Council under the Metatem project (GR/F/28526).Presented by Dov Gabbay     

Reasoning about actions and obligations in first-order logic

We describe a new way in which theories about the deontic status of actions can be represented in terms of the standard two-sorted first-order extensional predicate calculus. Some of the resulting formal theories are easy to implement in Prolog; one prototype implementation—R. M. Lee's deontic expert shell DX—is briefly described.This research was partially supported by the Esprit III Basic Research Working Group No. 8319 ModelAge.     

Doing well enough: Toward a logic for common-sense morality

On the traditional deontic framework, what is required (what morality demands) and what is optimal (what morality recommends) can't be distinguished and hence they can't both be represented. Although the morally optional can be represented, the supererogatory (exceeding morality's demands), one of its proper subclasses, cannot be. The morally indifferent, another proper subclass of the optional-one obviously disjoint from the supererogatory-is also not representable. Ditto for the permissibly suboptimal and the morally significant. Finally, the minimum that morality allows finds no place in the traditional scheme. With a focus on the question, “What would constitute a hospitable logical neighborhood for the concept of supererogation?”, I present and motivate an enriched logical and semantic framework for representing all these concepts of common sense morality.     

A Propositional Dynamic Logic with Qualitative Probabilities

This paper presents an -completeness theorem for a new propositional probabilistic logic, namely, the dynamic propositional logic of qualitative probabilities (D Q P), which has been introduced by the author as a dynamic extension of the logic of qualitative probabilities (Q P) introduced by Segerberg.     

Prolegomena of a Logic of Causality and Dynamism

We present in this article a new logical system inspired from linear logic. This system is designed in order to express causality and dynamism. The cut elimination theorem holds for this logic. Examples of applications are given.