First Order Logic With Domain Conditions

First Order Logic With Domain Conditions (2001)

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by Freek Wiedijk , Jan Zwanenburg

Venue:	in `Theorem Proving in Higher Order Logics, TPHOLs 2003', Vol. 2758 of LNCS
Citations:	2 - 0 self

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Datum	Value	Source
TITLE	First Order Logic With Domain Conditions	user correction - Legacy Corrections
AUTHOR NAME	Freek Wiedijk	user correction - Legacy Corrections
AUTHOR AFFIL	University of Nijmegen	user correction - Legacy Corrections
AUTHOR NAME	Jan Zwanenburg	user correction - Legacy Corrections
AUTHOR AFFIL	University of Nijmegen	user correction - Legacy Corrections
ABSTRACT	The correctness of proofs is increasingly being veried with computer programs called `proof checkers'. Examples of such proof checkers are Mizar, ACL2, PVS, Nuprl, HOL, Isabelle and Coq. This paper addresses what is one of the most important problems for that kind of system, which is how to deal with partial functions and the related issue of how to treat undened terms. In many systems the problem is avoided by articially making all functions total. However that does not correspond to the practice of every day mathematics. In type theory partial functions are modeled by giving functions extra arguments which are proof objects. Because of that it is not possible to apply a function outside its domain. However having proofs as rst class objects makes the logic non-standard. This has the disadvantages that it is unfamiliar to most mathematicians and that many proof tools won't be usable for it. For instance a theorem prover like Otter cannot be easily used for this kind of logic. Also expressions in type theoretical systems get clumsy because they contain proof objects. The PVS system solves the problem of partial functions dierently. PVS generates type-correctness conditions or TCCs for statements in its language. These are proof obligations that have to be satised `on the side' to show that the statements are well-formed. In this paper we relate the type theoretical approach to one resembling the PVS approach. We add domain conditions to ordinary rst order logic (which in this paper will be classical and one-sorted) and we show that the combination corresponds precisely to a rst order system that treats partial functions in the style of type theory. 1	user correction - Legacy Corrections
YEAR	2001	user correction - Legacy Corrections
VENUE	in `Theorem Proving in Higher Order Logics, TPHOLs 2003', Vol. 2758 of LNCS	INFERENCE
VENUE TYPE	CONFERENCE	INFERENCE
PAGES	221--237	INFERENCE
CITATIONS	16 found	ParsCit 1.0