19 research outputs found
Logical presentations of domains
Bibliography: pages 168-174.This thesis combines a fairly general overview of domain theory with a detailed examination of recent work which establishes a connection between domain theory and logic. To start with, the theory of domains is developed with such issues as the semantics of recursion and iteration; the solution of recursive domain equations; and non-determinism in mind. In this way, a reasonably comprehensive account of domains, as ordered sets, is given. The topological dimension of domain theory is then revealed, and the logical insights gained by regarding domains as topological spaces are emphasised. These logical insights are further reinforced by an examination of pointless topology and Stone duality. A few of the more prominent categories of domains are surveyed, and Stone-type dualities for the objects of some of these categories are presented. The above dualities are then applied to the task of presenting domains as logical theories. Two types of logical theory are considered, namely axiomatic systems, and Gentzen-style deductive systems. The way in which these theories describe domains is by capturing the relationships between the open subsets of domains
The temporal logic of two-dimensional Minkowski spacetime with slower-than-light accessibility is decidable
We work primarily with the Kripke frame consisting of two-dimensional
Minkowski spacetime with the irreflexive accessibility relation 'can reach with
a slower-than-light signal'. We show that in the basic temporal language, the
set of validities over this frame is decidable. We then refine this to
PSPACE-complete. In both cases the same result for the corresponding reflexive
frame follows immediately. With a little more work we obtain
PSPACE-completeness for the validities of the Halpern-Shoham logic of intervals
on the real line with two different combinations of modalities.Comment: 20 page
Experiments in Theorem Proving for Topological Hybrid Logic
International audienceThis paper discusses two experiments in theorem proving for hybrid logic under the topological interpre-tation. We begin by discussing the topological interpretation of hybrid logic and noting what it adds to the topological interpretation of orthodox modal logic. We then examine two implemented proof methods. The first makes use of HyLoBan, a terminating theorem prover that searches for a winning search strategy in certain topologically motivated games. The second is a translation-based approach that makes use of HyLoTab, a tableaux-based theorem prover for hybrid logic under the standard relational interpretation. We compare the two methods, and note a number of directions for further work