Results 1  10
of
11
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 ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
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...
Conceptual Models and Computing
, 1990
"... I declare that this thesis has not been submitted as an exercise for a degree at any other University. I declare that all of the material contained herein is entirely my own work. I declare my consent to the Library of Trinity College, Dublin, that I agree that the Library may lend or copy this thes ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
I declare that this thesis has not been submitted as an exercise for a degree at any other University. I declare that all of the material contained herein is entirely my own work. I declare my consent to the Library of Trinity College, Dublin, that I agree that the Library may lend or copy this thesis upon request. Signature: M. Mac an Airchinnigh Date: 3 October 1990Summary Human beings form conceptual models of their world and behave accordingly. I have focused my research on those aspects of conceptual models which are peculiar to the act of computing and with particular reference to the specification, design and development of software which is intended to be executed on a computer. The conceptual models of mathematicians and computing scientists have much in common. I argue that software engineers should develop a similar kind of conceptual model, one which is founded on discrete mathematics and mathematical method. I have identified the central rôle that
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 ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
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 &quot;ordered covering&quot;, 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 &quot;on variables &quot; and use of heuristics, and the rewritebased induction &quot;on subterms &quot; 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 ..."
Abstract
 Add to MetaCart
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
 Add to MetaCart
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
 Add to MetaCart
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
Formal Mathematical Systems including a Structural Induction Principle
, 2005
"... This study provides a general frame for the generation of languages in recursive systems closely related to formal grammars, for the predicate calculus and a constructive induction principle. We introduce recursive systems generating the recursively enumerable relations between lists of terms, the b ..."
Abstract
 Add to MetaCart
This study provides a general frame for the generation of languages in recursive systems closely related to formal grammars, for the predicate calculus and a constructive induction principle. We introduce recursive systems generating the recursively enumerable relations between lists of terms, the basic objects under consideration. A recursive system consists of axioms which are special quantifierfree positive horn formulas and of special rules of inference. Its extension to formal mathematical systems includes the predicate calculus as well as a structural induction principle with respect to the axioms of the underlying recursive system. We have also formulated our main results about elementary proof theory for quite general restrictions in the argument lists of the formulas, which enables different kind of applications. 0