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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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Cited by 33 (25 self)
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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 algebraic behav ..."
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Cited by 1 (0 self)
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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 #...
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 receive a ..."
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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
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 (ecthesis), and that ther ..."
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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 StÃ¶rring (1908) to the present day. It was hypothesised that by rendering