Completeness of neighbourhood logic

Completeness of Neighbourhood Logic

This paper presents a completeness result for a first-order interval temporal logic, called Neighbourhood Logic (NL) which has two neighbourhood modalities. NL can support the specification of liveness and fairness properties of computing systems as well as formalisation of many concepts of real analysis. These two modalities are also adequate in the sense that they can derive other important u...

Algebraic Neighbourhood Logic

We present an algebraic embedding of Neighbourhood Logic (NL) into the framework of semirings which yields various simplifications. For example, some of the NL axioms can be dropped, since they are theorems in our framework, and Galois connections produce properties for free. A further simplification is achieved, since the semiring methods used are easy and fairly standard. Moreover, this embed...

Probabilistic Neighbourhood Logic

This paper presents a probabilistic extension of Neighbourhood Logic (NL,[14, 1]). The study of such an extension is motivated by the need to supply the Probabilistic Duration Calculus (PDC, [10, 4]) with a proof system. The relation between the new logic and PDC is similar to that between DC [15] and ITL [12, 3]. We present a complete proof system for the new logic.

Instantial Neighbourhood Logic

This paper explores a new language of neighbourhood structures where existential information can be given about what kind of worlds occur in a neighbourhood of a current world. The resulting system of ‘instantial neighbourhood logic’ INL has a non-trivial mix of features from relational semantics and from neighbourhood semantics. We explore some basic model-theoretic behavior, including a match...

Completeness in modal logic