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Constructivism and Proof Theory
, 2003
"... Introduction to the constructive point of view in the foundations of mathematics, in
particular intuitionism due to L.E.J. Brouwer, constructive recursive mathematics
due to A.A. Markov, and Bishop’s constructive mathematics. The constructive interpretation
and formalization of logic is described. F ..."
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Cited by 204 (4 self)
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Introduction to the constructive point of view in the foundations of mathematics, in
particular intuitionism due to L.E.J. Brouwer, constructive recursive mathematics
due to A.A. Markov, and Bishop’s constructive mathematics. The constructive interpretation
and formalization of logic is described. For constructive (intuitionistic)
arithmetic, Kleene’s realizability interpretation is given; this provides an example
of the possibility of a constructive mathematical practice which diverges from classical
mathematics. The crucial notion in intuitionistic analysis, choice sequence, is
briefly described and some principles which are valid for choice sequences are discussed.
The second half of the article deals with some aspects of proof theory, i.e.,
the study of formal proofs as combinatorial objects. Gentzen’s fundamental contributions
are outlined: his introduction of the socalled Gentzen systems which use
sequents instead of formulas and his result on firstorder arithmetic showing that
(suitably formalized) transfinite induction up to the ordinal "0 cannot be proved in
firstorder arithmetic.
Reasoning with temporal logic on truncated paths
 In: CAV’03. LNCS 2725
, 2003
"... Abstract. We consider the problem of reasoning with linear temporal logic on truncated paths. A truncated path is a path that is finite, but not necessarily maximal. Truncated paths arise naturally in several areas, among which are incomplete verification methods (such as simulation or bounded model ..."
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Cited by 27 (4 self)
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Abstract. We consider the problem of reasoning with linear temporal logic on truncated paths. A truncated path is a path that is finite, but not necessarily maximal. Truncated paths arise naturally in several areas, among which are incomplete verification methods (such as simulation or bounded model checking) and hardware resets. We present a formalism for reasoning about truncated paths, and analyze its characteristics. 1
Geology of London
 Memoir of the British Geological Survey, Sheets 256 (North London), 257 (Romford), 270 (South London) and 271
, 2004
"... Abstract: In criminal cases at common law, juries are permitted to convict on wholly circumstantial evidence even in the face of a reasonable case for acquittal. This generates the highly counterintuitive—if not absurd— consequence that there being reason to think that the accused didn’t do it is no ..."
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Cited by 9 (0 self)
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Abstract: In criminal cases at common law, juries are permitted to convict on wholly circumstantial evidence even in the face of a reasonable case for acquittal. This generates the highly counterintuitive—if not absurd— consequence that there being reason to think that the accused didn’t do it is not reason to doubt that he did. This is the noreasontodoubt problem. It has a technical solution provided that the evidence on which it is reasonable to think that the accused didn’t do it is a different subset of the total evidence from that on which there is no reason to doubt that he did do it. It lies in the adversarial nature of criminal proceedings in the common law tradition that the subsets of the total evidence on which counsel base their opposing arguments are themselves different from and often incompatible with one another. While this solves the noreasontodoubt problem, it does so at the cost of triggering a second problem just as bad. It is the norival problem, according to which incompatible theories of the case based on incompatible subsets of the evidence cannot be rivals of one another. If neither party’s case contradicts the other’s then, by the burden of proof requirement, criminal convictions are impossible. Once having generated the dilemma, the object of the paper is to determine how it might be escaped.
The combination of paradoxical, uncertain and imprecise sources of information based on DSmT and neutrofuzzy inference
 Journal of Applied Mathematics & Computing, Seoul, South Korea
, 2005
"... Abstract – The management and combination of uncertain, imprecise, fuzzy and even paradoxical or high conflicting sources of information has always been, and still remains today, of primal importance for the development of reliable modern information systems involving artificial reasoning. In this c ..."
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Abstract – The management and combination of uncertain, imprecise, fuzzy and even paradoxical or high conflicting sources of information has always been, and still remains today, of primal importance for the development of reliable modern information systems involving artificial reasoning. In this chapter, we present a survey of our recent theory of plausible and paradoxical reasoning, known as DezertSmarandache Theory (DSmT) in the literature, developed for dealing with imprecise, uncertain and paradoxical sources of information. We focus our presentation here rather on the foundations of DSmT, and on the two important new rules of combination, than on browsing specific applications of DSmT available in literature. Several simple examples are given throughout the presentation to show the efficiency and the generality of this new approach. The last part of this chapter concerns the presentation of the neutrosophic logic, the neutrofuzzy inference and its connection with DSmT. Fuzzy logic and neutrosophic logic are useful tools in decision making after fusioning the information using the DSm hybrid rule of combination of masses.
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