Max Wisniewski

LeoPARD -- A Generic Platform for the Implementation of Higher-Order Reasoners

LeoPARD supports the implementation of knowledge representation and reasoning tools for higher-order logic(s). It combines a sophisticated data structure layer (polymorphically typed {\lambda}-calculus with nameless spine notation, explicit substitutions, and perfect term sharing) with an ambitious multi-agent blackboard architecture (supporting prover parallelism at the term, clause, and search level). Further features of LeoPARD include a parser for all TPTP dialects, a command line interpreter, and generic means for the integration of external reasoners.

Agent-Based HOL Reasoning

In the Leo-III project, a new agent-based deduction system for classical higher-order logic is developed. Leo-III combines its predecessor’s concept of cooperating external specialist systems with a novel agent-based proof procedure. Key goals of the system’s development involve parallelism on various levels of the proof search, adaptability for different external specialists, and native support for reasoning in expressive non-classical logics.

Effective Normalization Techniques for HOL

Normalization procedures are an important component of most automated theorem provers. In this work we present an adaption of advanced first-order normalization techniques for higher-order theorem proving which have been bundled in a stand-alone tool. It can be used in conjunction with any higher-order theorem prover, even though the implemented techniques are primarily targeted on resolution-based provers. We evaluated the normalization procedure on selected problems of the TPTP using multiple HO ATPs. The results show a significant performance increase, in both speed and proving capabilities, for some of the tested problem instances.