In this paper we present our work in progress towards obtaining a Nelson-Oppen style combination for combining quantified theories, where each individual component theory admits quantifier elimination. We introduces the notion of good model for union theories, for which there exists a simple quantifier elimination scheme that uses the elimination procedures for individual component theories as ...

A biform theory is a combination of an axiomatic theory and an algorithmic theory that supports the integration of reasoning and computation. These are ideal for formalizing algorithms that manipulate mathematical expressions. A theory graph is a network of theories connected by meaning-preserving theory morphisms that map the formulas of one theory to the formulas of another theory. Theory gra...

This study examined the relationship between the external representation, verbal encoding vs. visual encoding, of graph information and the impact on graph comprehension. Graph comprehension tasks included responses to true/false statements addressing global and local graph information, visual recognition, and graph drawing. The findings suggest that the specific modality of the external repres...

Within the Unifying Theories of Programming framework, program initiation and termination has been modelled by introducing a pair of variables in order to satisfy the required algebraic properties. We replace these variables with the improper value ⊥ that is frequently used to denote undefinedness. Both approaches are proved isomorphic using the relation calculus, and the existing operations an...

In this paper we give an outline of recent results concerning theories and models of the untyped lambda calculus. Algebraic and topological methods have been applied to study the structure of the lattice of λ-theories, the equational incompleteness of lambda calculus semantics, and the λ-theories induced by graph models of lambda calculus.

The current theories of graph comprehension have posited the graph schema as providing us the necessary knowledge to interpret any graph type. Yet, little is known about the nature of the graph schema, and no empirical data exist showing that there actually is a graph schema. In experiment 1 we show evidence that a graph schema does exist, and that graph schemas are not specific to each and eve...

We consider the problem of characterizing the finitely additive probability measures on the definable subsets of the random graph which are invariant under the action of the automorphism group of this graph. We show that such measures are all integrals of Bernoulli measures (which arise from the coin-flipping model of the construction of the random graph). We also discuss generalizations to oth...