Deductive software as opposed to numerical software is gaining more and more importance in industrial applications. Numerical software can be found in components prevalent in control systems that are built into cars, trains, space vehicles, and plants, recognition systems for voice, vision, and access control, but also our internet infrastructure such as load balancing servers, and routers. Reg...

Using some routine properties ([zu], [po]) of the Prawitz translation φ from (sequent calculus) derivations to (natural) deductions, and restricting ourselves to the language of first-order hereditary Harrop formulae, we show (i) that φ maps the simple uniform derivations of Miller et al onto the set of deductions in expanded normal form; and (ii) that φ identifies two such derivations iff they...

Guidance is a central issue in Automatic Theorem Proving systems due to the enormity of the search space that these systems navigate. Semantic guidance uses semantic information to direct the path an ATP system takes through the search space. The use of semantic information is potentially more powerful than syntactic information for guidance. This research aimed to discover a method for incorpo...

Intuitionistic proofs can be segmented into scopes which describe when assumptions can be used. In standard descriptions of intuitionistic logic, these scopes occupy contiguous regions of proofs. This leads to an explosion in the search space for automated deduction, because of the difficulty of planning to apply a rule inside a particular scoped region of the proof. This paper investigates an ...

In this paper we offer a system J-Calc that can be regarded as a typed λ-calculus for the {→,⊥} fragment of Intuitionistic Justification Logic. We offer different interpretations of J-Calc, in particular, as a two phase proof system in which we proof check the validity of deductions of a theory T based on deductions from a stronger theory T ′ and computationally as a type system for separate co...

This paper presents an algorithm for simplifying NDL deductions. An array of simplifying transformations are rigorously defined. They are shown to be terminating, and to respect the formal semantics of the language. We also show that the transformations never increase the size or complexity of a deduction—in the worst case, they produce deductions of the same size and complexity as the original...