Mathematics can provide precise formulations of relatively vague concepts and problems from the real world, and bring out underlying structure common to diverse scientific areas. Sometimes very natural mathematical concepts lie neglected and not widely understood for many years, before their fundamental relevance is recognised and their explanatory power is fully exploited. The notion of defina...

We study the first order theory of structures over graphs i.e. structures of the form (G, τ ) where G is the set of all (isomorphism types of) finite undirected graphs and τ some vocabulary. We define the notion of a recursive predicate over graphs using Turing Machine recognizable string encodings of graphs. We introduce the notion of a capable structure over graphs, which is one satisfying th...

Understanding modal predicate logic is a continuing challenge, both philosophical and mathematical. In this paper, I study this system in terms of frame correspondences, finding a number of definability results using substitution methods, including new analyses of axioms in intermediate intuitionistic predicate logics. The semantic arguments often have a different flavour from those in proposit...

A formal framework is given for the postulate characterizability of a class of belief revision operators, obtained from a class of partial preorders using minimization. It is shown that for classes of posets characterizability is equivalent to a special kind of definability in monadic second-order logic, which turns out to be incomparable to first-order definability. Several examples are given ...

We derive author's discrete forms of the Beckman-Quarles theorem from the definability results of Raphael M. Robinson. The classical Beckman-Quarles theorem states that each map from R n to R n (n > 1) preserving all unit distances is an isometry, see [1]-[3]. In this note we derive author's discrete forms of this theorem ([6]) from the definability results of Raphael M. Robinson (see [4] and a...