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From inheritance relation to nonaxiomatic logic
 International Journal of Approximate Reasoning
, 1994
"... NonAxiomatic Reasoning System is an adaptive system that works with insu cient knowledge and resources. At the beginning of the paper, three binary term logics are de ned. The rst is based only on an inheritance relation. The second and the third suggest a novel way to process extension and intensi ..."
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NonAxiomatic Reasoning System is an adaptive system that works with insu cient knowledge and resources. At the beginning of the paper, three binary term logics are de ned. The rst is based only on an inheritance relation. The second and the third suggest a novel way to process extension and intension, and they also have interesting relations with Aristotle's syllogistic logic. Based on the three simple systems, a NonAxiomatic Logic is de ned. It has a termoriented language and an experiencegrounded semantics. It can uniformly represents and processes randomness, fuzziness, and ignorance. It can also uniformly carries out deduction, abduction, induction, and revision.
On Lukasiewicz's fourvalued modal logic
, 2000
"... . # Lukasiewicz's fourvalued modal logic is surveyed and analyzed, together with # Lukasiewicz's motivations to develop it. A faithful interpretation of it into classical (nonmodal) twovalued logic is presented, and some consequences are drawn concerning its classification and its algeb ..."
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. # Lukasiewicz's fourvalued modal logic is surveyed and analyzed, together with # Lukasiewicz's motivations to develop it. A faithful interpretation of it into classical (nonmodal) twovalued logic is presented, and some consequences are drawn concerning its classification and its algebraic behaviour. Some counterintuitive aspects of this logic are discussed under the light of the presented results, # Lukasiewicz's own texts, and related literature. 1 Introduction The Polish philosopher and logician Jan # Lukasiewicz (Lwow, 1878  Dublin, 1956) is one of the fathers of modern manyvalued logic, and some of the systems he introduced are presently a topic of deep investigation. In particular his infinitelyvalued logic belongs to the core systems of mathematical fuzzy logic as a logic of comparative truth, see [5, 15, 14, 16]. However, it must be stressed here that # Lukasiewicz's logical work bears also a special relationship to modal logic. Actually, modal notions were part of #...
Solving Categorical Syllogisms with Singular Premises
"... We elaborate on the approach to syllogistic reasoning based on "case identification " (Stenning & Oberlander, 1995; Stenning & Yule, 1997). It is shown that this can be viewed as the formalisation of a method of proof that dates back to Aristotle, namely proof by exposition (ecthes ..."
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We elaborate on the approach to syllogistic reasoning based on "case identification " (Stenning & Oberlander, 1995; Stenning & Yule, 1997). It is shown that this can be viewed as the formalisation of a method of proof that dates back to Aristotle, namely proof by exposition (ecthesis), and that there are traces of this method in the strategies described by a number of psychologists, from Störring (1908) to the present day. It was hypothesised that by rendering
Aristotle and Lukasiewicz on Existential Import∗
, 2015
"... Jan Lukasiewicz’s treatise on Aristotle’s Syllogistic, published in the 1950s, has been very influential in framing contemporary understanding of Aristotle’s logical systems. However, Lukasiewicz’s interpretation is based on a number of tendentious claims, not least, the claim that the syllogisti ..."
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Jan Lukasiewicz’s treatise on Aristotle’s Syllogistic, published in the 1950s, has been very influential in framing contemporary understanding of Aristotle’s logical systems. However, Lukasiewicz’s interpretation is based on a number of tendentious claims, not least, the claim that the syllogistic was intended to apply only to nonempty terms. I show that this interpretation is not true to Aristotle’s text and that a more coherent and faithful interpretation admits empty terms while maintaining all the relations of the traditional square of opposition. There is a widespread account of Aristotle’s logic which claims that it applies only to nonempty terms. We find it recently endorsed in, e.g., the Stanford Encyclopedia article on ‘Aristotle’s Logic’: “[According to Aristotle] we can get ‘Some monsters are chimeras’ from the apparently true ‘All chimeras are monsters’; but the former is often construed as implying in turn ‘There is some
(pp. 214240). Hove: Psychology Press.
"... Some precursors of current theories of syllogistic reasoning ..."
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An Evidential Path Logic for MultiRelational Networks
, 810
"... Multirelational networks are used extensively to structure knowledge. Perhaps the most popular instance, due to the widespread adoption of the Semantic Web, is the Resource Description Framework (RDF). One of the primary purposes of a knowledge network is to reason; that is, to alter the topology o ..."
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Multirelational networks are used extensively to structure knowledge. Perhaps the most popular instance, due to the widespread adoption of the Semantic Web, is the Resource Description Framework (RDF). One of the primary purposes of a knowledge network is to reason; that is, to alter the topology of the network according to an algorithm that uses the existing topological structure as its input. There exist many such reasoning algorithms. With respect to the Semantic Web, the bivalent, monotonic reasoners of the RDF Schema (RDFS) and the Web Ontology Language (OWL) are the most prevalent. However, nothing prevents other forms of reasoning from existing in the Semantic Web. This article presents a nonbivalent, nonmonotonic, evidential
Solving Natural Syllogisms
"... The oldest reasoning task ever studied by psychologists is categorical syllogisms. One may question whether after a century of investigation there is still something to be learned about people's deductive competence from research on syllogistic reasoning. In this chapter this question will rece ..."
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The oldest reasoning task ever studied by psychologists is categorical syllogisms. One may question whether after a century of investigation there is still something to be learned about people's deductive competence from research on syllogistic reasoning. In this chapter this question will receive a double answer: a negative answer as far as the usual laboratory task is concerned, as it will be claimed that it has been deeply misused; but also an affirmative answer in the sense that previous research has ignored the ecological relevance of syllogisms: this has often been denied but it will be argued that this stems from a fallacious conception of the epistemological status of the formal arguments and from a subsequent bias in their instantiation. Finally, it will be shown that lay people are highly competent and successful in using syllogisms once a methodological precaution has been taken, which turns the arguments into natural syllogisms satisfying the demand of ecological validity. NATURAL SYLLOGISMS AND THE STATUS OF FORMAL SYLLOGISMS
ANCESTOR WORSHIP IN THE LOGIC OF GAMES HOW FOUNDATIONAL WERE ARISTOTLE’S
"... ABSTRACT: Notwithstanding their technical virtuosity and growing presence in mainstream thinking, game theoretic logics have attracted a sceptical question: “Granted that logic can be done game theoretically, but what would justify the idea that this is the preferred way to do it? ” A recent sugges ..."
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ABSTRACT: Notwithstanding their technical virtuosity and growing presence in mainstream thinking, game theoretic logics have attracted a sceptical question: “Granted that logic can be done game theoretically, but what would justify the idea that this is the preferred way to do it? ” A recent suggestion is that at least part of the desired support might be found in the Greek dialectical writings. If so, perhaps we could say that those works possess a kind of foundational significance. The relation of being foundational for is interesting in its own right. In this paper, I explore its ancient applicability to relevant, paraconsistent and nonmonotonic logics, before returning to the question of its ancestral tie, or want of one, to the modern logics of games. 1. LOGIC AND GAME THEORY Since its inception in the early 1940s (von Neumann & Morgenstern 1944),1 the mathematical theory of games has become something of