This paper studies the concepts of definability and canonicity in Boolean logic with a binary relation. Firstly, it provides formulas defining first-order or second-order conditions on frames. Secondly, it proves that all formulas corresponding to compatible first-order conditions on frames are canonical.

In preference aggregation a set of individuals express preferences over a set of alternatives, and these preferences have to be aggregated into a collective preference. When preferences are represented as orders, aggregation procedures are called social welfare functions. Classical results in social choice theory state that it is impossible to aggregate the preferences of a set of individuals u...

A language L over an alphabet A is said to have a neutral letter if there is a letter e ∈ A such that inserting or deleting e’s from any word inA does not change its membership (or non–membership) in L. The presence of a neutral letter affects the definability of a language in first–order logic. It was conjectured that it renders all numerical predicates apart from the order predicate useless, ...

The purpose of this article is to delimit what can and cannot be claimed on behalf of second-order logic. The starting point is some of the discussions surrounding my Foundations without Foundationalism: A Case for Second-

We present a clausal connection calculus for first-order intuitionistic logic. It extends the classical connection calculus by adding prefixes that encode the characteristics of intuitionistic logic. Our calculus is based on a clausal matrix characterisation for intuitionistic logic, which we prove correct and complete. The calculus was implemented by extending the classical prover leanCoP. We ...

The Loś-Tarski Theorem and the ChangLoś-Susko Theorem, two classical results in Model Theory, are extended to the infinitevalued Lukasiewicz logic. The latter is used to settle a characterisation of the class of generic structures introduced in the framework of model theoretic forcing for Lukasiewicz logic [1]. Key-words: First Order Many-Valued Logic, Lukasiewicz logic, Model Theory.

Let K be a set of n non-intersecting objects in 3-space. A depth order of K, if exists, is a linear order < of the objects in K such that if K; L 2 K and K lies vertically below L then K < L. We present a new technique for computing depth orders, and apply it to several special classes of objects. Our results include: (i) If K is a set of n triangles whose xy-projections are alìfat', then a dep...

We introduce a version of logic for metric structures suitable for applications to C*-algebras and tracial von Neumann algebras. We also prove a purely model-theoretic result to the effect that the theory of a separable metric structure is stable if and only if all of its ultrapowers associated with nonprincipal ultrafilters on N are isomorphic even when the Continuum Hypothesis fails.

Behavioural logic is a generalization of first-order logic where the equality predicate is interpreted by a behavioural equality of objects (and not by their identity). We establish simple and general sufficient conditions under which the behavioural validity of some first-order formula with respect to a given first-order specification is equivalent to the standard validity of the same formula ...

This paper characterizes the expressive power of a subclass of first-order logical decision trees (FOLDTs) as a fragment of firstorder logic. Specifically, using safe FOLDTs one can express precisely the boolean combinations of safe existential sentences.