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Proof Theory of Finitevalued Logics
, 1993
"... Manyvalued logic is not much younger than the whole field of symbolic logic. It was introduced in the early twenties of this century by ̷Lukasiewicz [1920] and Post [1921] and has since developed into a very large area of research. Most of the early work done has concentrated on problems of axiomat ..."
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Cited by 6 (1 self)
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Manyvalued logic is not much younger than the whole field of symbolic logic. It was introduced in the early twenties of this century by ̷Lukasiewicz [1920] and Post [1921] and has since developed into a very large area of research. Most of the early work done has concentrated on problems of axiomatizability on the one hand, and algebraical/model theoretic investigations on the other. The proof theory of manyvalued systems has not been investigated to any comparable extent. Proof theory requires appropriate formalisms, such as sequent calculus, natural deduction, and tableaux for classical (and intuitionistic) logic. Several people have, since the 1950’s, proposed ways to generalize such formalisms from the classical to the manyvalued case. One particular method for systematically obtaining calculi for all finitevalued logics was invented independently by several researchers, with slight variations in design and presentation. (Section 3.1 contains a short overview of work done in this area). The main aim of this report is to develop the proof theory of finitevalued first order logics in a
Effective Metaprogramming in Declarative Languages
, 1998
"... Declarative metaprogramming is vital, since it is the most promising means by which programs can be made to reason about other programs. A metaprogram is a program that takes another program, called the object program, as data. A declarative programming language is a programming language based on a ..."
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Cited by 2 (0 self)
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Declarative metaprogramming is vital, since it is the most promising means by which programs can be made to reason about other programs. A metaprogram is a program that takes another program, called the object program, as data. A declarative programming language is a programming language based on a logic that has a model theory. A metaprogram operates on a representation of an object...
A project to develop an inductive proof assistant for Z integrating classical and rewrite strategies
, 1997
"... Z is a formal specification language that is extensively used in both academia and industry. Several tools have been developed for reasoning about Z specifications, but they all lack substantial facilities for inductive reasoning. We propose the development of such a reasoning assistant for Z. Utili ..."
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Z is a formal specification language that is extensively used in both academia and industry. Several tools have been developed for reasoning about Z specifications, but they all lack substantial facilities for inductive reasoning. We propose the development of such a reasoning assistant for Z. Utilising the concept of "ordered covering", our proposed approach will combine aspects of both the classical and rewritebased approaches to proof by induction. In particular, it will include the classical induction "on variables " and use of heuristics, and the rewritebased induction "on subterms " and unification for generation of induction cases. In this way, we will not only be developing an inductive reasoner for Z but will be furthering our understanding of the automation of proof by induction. To ensure that our reasoning principles and strategies are appropriate for Z, we propose to implement them in CADiZ, an interactive reasoning tool for Z developed at the University of York. We will evaluate the utility of the resulting system by attempting to construct a broad range of proofs, including some of practical importance to computer security, safetycritical systems and compiler correctness.
unknown title
, 2009
"... The significance of Nathanson’s boss factor in legitimising Aristotle’s particularisation Why we need to revise current interpretations of Cantor’s, Gödel’s, Turing’s and Tarski’s formal reasoning ..."
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The significance of Nathanson’s boss factor in legitimising Aristotle’s particularisation Why we need to revise current interpretations of Cantor’s, Gödel’s, Turing’s and Tarski’s formal reasoning
unknown title
, 2009
"... The significance of Nathanson’s boss factor in legitimising Aristotle’s particularisation Why we need to revise current interpretations of Cantor’s, Gödel’s, Turing’s and Tarski’s formal reasoning ..."
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The significance of Nathanson’s boss factor in legitimising Aristotle’s particularisation Why we need to revise current interpretations of Cantor’s, Gödel’s, Turing’s and Tarski’s formal reasoning
unknown title
, 2009
"... The significance of Nathanson’s boss factor in legitimising Aristotle’s particularisation Why we need to revise current interpretations of Cantor’s, Gödel’s, Turing’s and Tarski’s formal reasoning ..."
Abstract
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The significance of Nathanson’s boss factor in legitimising Aristotle’s particularisation Why we need to revise current interpretations of Cantor’s, Gödel’s, Turing’s and Tarski’s formal reasoning