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Title: Proof planning with logic presentations
Author: Negrete-Yankelevich, Santiago
Awarding Body: University of Edinburgh
Current Institution: University of Edinburgh
Date of Award: 1997
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Logic has proven to be of prime importance in many areas of Science and, in particular, in AI and Computer Science. Many logics have been developed to contend with the various kinds of reasoning required by a vast number of research areas. Automatic theorem proving techniques for these logics are often developed in an ad-hoc way for particular theories in which specific problems are representable. Framework logics have been proposed as meta-mathematical theories in which other theories may be represented and reasoned with uniformly. Hence, automating proof search in a framework logic gives the possibility of abstracting the proof process and makes it applicable to a larger number of logics. In this thesis, we introduce an approach to proof search in the Edinburgh Logical Framework that is not hard-wired to a particular object logic. The design is based on guiding proof search through constrained rewriting. The rewriting technique is called Rippling; it has been previously applied to the domain of inductive proofs within the framework of Proof Plans. This approach consists of building proof plans for theorems from abstract specifications of proof techniques called Methods. Methods correspond to tactics programmed in a Proof Editor where the theorem can be represented and where a proof plan can be realised to construct the actual proof for the theorem. Our work is focused on logic presentations and we have extended the Rippling technique in various ways to handle this more general case. A feature of our approach is that, since the rewrite rules used in Rippling are extracted from the logic presentation in the framework logic, the proof mechanisms are independent of the logic at hand. We have conducted experiments in various classical and non-classical logics and conjecture that our methodology is applicable to frameworks and logics other than those we have explored here.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available