We present a Prolog program that implements a sound and complete theorem prover for first-order intuitionistic logic. It is based on free-variable semantic tableaux extended by an additional string unification to ensure the particular restrictions in intuitionistic logic. Due to the modular treatment of the different logical connectives the implementation can easily be adapted to deal with othe...

This paper presents a novel analysis of bound variable anaphora using Synchronous Tree Adjoining Grammar (STAG), a pairing of a Tree Adjoining Grammar (TAG) for syntax and a TAG for semantics. While a bound variable pronoun can occur at a distance from its binder, as in ‘Every girli believes that shei is intelligent,’ languages vary, though in a limited way, as to how near or far from its binde...

In this paper, we show how an approach to belief revision and belief contraction can be axiomatised by means of quantified Boolean formulas. Specifically, we consider the approach of belief change scenarios, a general framework that has been introduced for expressing different forms of belief change. The essential idea is that for a belief change scenario (K, R, C), the set of formulas K, repre...

We study the representation of the solutions of a polynomial system by triangular sets, and concentrate on the positive-dimensional case. We reduce to dimension zero by placing the free variables in the base field, so the solutions can be represented by triangular sets with coefficients in a rational function field. We give intrinsic-type bounds on the degree of the coefficients in such a trian...

The celebrated theorem proved by Goldblatt and Thomason in 1974 gives necessary and sufficient conditions for an elementary (i.e., first-order definable) class of Kripke frames to be modally definable. Here we obtain a local analogue of this result, where in place of frames we consider n-frames, which are frames with n distinguished worlds. For talking about n-frames, we generalize customary mo...

E-matching is the most commonly used technique to handle quantifiers in SMT solvers. It works by identifying characteristic subexpressions of quantified formulae, named triggers, which are matched during proof search on ground terms to discover relevant instantiations of the quantified formula. E-matching has proven to be an efficient and practical approach to handle quantifiers, in particular ...

A notation for probabilities is proposed that differs from the traditional, conventional notation by making explicit the domains and bound variables involved. The notation borrows from the Z notation, and lends itself well to calculational manipulations, with a smooth transition back and forth to set and predicate notation.

Away is found to add axioms to sequent calculi that maintains the eliminability of cut, through the representation of axioms as rules of inference of a suitable form. By this method, the structural analysis of proofs is extended from pure logic to free-variable theories, covering all classical theories, and a wide class of constructive theories. All results are proved for systems in which also ...

In this paper we propose higher-order rewrite systems without bound variables. In order to prove their connuence under the assumption of orthogonality, we study a simple proof method which employs a characterization of the diamond property of a parallel reduction. By an application of the proof method, we obtain a new connuence result for orthogonal higher-order conditional rewrite systems.

Every theory we will consider will be in a language that has a name ṅ for each n ∈ ω. For example, the name for 2 ∈ ω in the language LΩ of arithmetic is the term “1 + 1”. The results stated will only apply to countable languages. This requirement is implicit in the hypothesis of the existence of an enumeration of all formulas with one free variable, for example. We also assume that formulas an...