The world of lexis is vast and complex and it is generally accepted in psycholinguistics that it is represented as part of a large complex network. However, in systemic functional linguistics (SFL) modelling lexis has remained a relatively underdeveloped area of the theory. The ideas underpinning this paper stem from exploring the interface of context and lexicology, asking how SFL does and cou...

We present a method which computes optimized representations for non-convex polyhedra. Our method detects so-called redundant linear constraints in these representations by using an incremental SMT (Satisfiability Modulo Theories) solver and then removes the redundant constraints based on Craig interpolation. The approach is motivated by applications in the context of model checking for Linear ...

In this paper we present a semantic embedding of Hoare and He’s Unifying Theories of Programming (UTP) framework into the ProofPower-Z theorem prover; it concisely captures the notion of UTP theory, theory instantiation, and, additionally, type restrictions on the alphabet. We show how the encoding can be used to reason about UTP theories and their predicates, including models of particular spe...

In this paper we concentrate on open problems in two directions in the development of the theory of constructive algebraic systems. The first direction deals with universal algebras whose positive open diagrams can be computably enumerated. These algebras are called positive algebras. Here we emphasize the interplay between universal algebra and computability theory. We propose a systematic stu...

Circus combines elements from sequential and reactive programming, and is especially suited for the development and verification of state-rich, reactive systems. In this paper we illustrate, by example, how a mechanisation of the UTP, and of a Circus theory, more specifically, can be used to encode particular Circus specifications. This complements previous work which focused on using the mecha...

Satisfiability Modulo Theories (SMT) solvers have proven highly scalable, efficient and suitable for integrating theory reasoning. However, for numerous applications from program analysis and verification, the ground fragment is insufficient, as proof obligations often include quantifiers. A well known approach for quantifier reasoning uses a matching algorithm that works against an E-graph to ...

Satisfiability Modulo Theories (SMT) solvers have proven highly scalable, efficient and suitable for integrated theory reasoning. The most efficient SMT solvers rely on refutationally incomplete methods for incorporating quantifier reasoning. We describe a calculus and a system that tightly integrates Superposition and DPLL(T). In the calculus, all non-unit ground clauses are delegated to the D...

We present a new method for interpolation in satisfiability modulo theories (SMT) that is aimed at applications in model-checking and invariant inference. The new method allows us to control the finiteconvergence of interpolant sequences and, at the same time, provides expressive invariant-driven interpolants. It is based on a novel integration of model-driven quantifier elimination and abstrac...

In this paper we explain the design and preliminary implementation of a solver for the positive satisfiability problem of concepts in a fuzzy description logic over the infinite-valued product logic. This very solver also answers 1-satisfiability in quasi-witnessed models. The solver works by first performing a direct reduction of the problem to a satisfiability problem of a quantifier free boo...