The Fuzzy Syllogistic System
نویسندگان
چکیده
A categorical syllogism is a rule of inference, consisting of two premisses and one conclusion. Every premiss and conclusion consists of dual relationships between the objects M, P, S. Logicians usually use only true syllogisms for deductive reasoning. After predicate logic had superseded syllogisms in the 19th century, interest on the syllogistic system vanished. We have analysed the syllogistic system, which consists of 256 syllogistic moods in total, algorithmically. We have discovered that the symmetric structure of syllogistic figure formation is inherited to the moods and their truth values, making the syllogistic system an inherently symmetric reasoning mechanism, consisting of 25 true, 100 unlikely, 6 uncertain, 100 likely and 25 false moods. In this contribution, we discuss the most significant statistical properties of the syllogistic system and define on top of that the fuzzy syllogistic system. The fuzzy syllogistic system allows for syllogistic approximate reasoning inductively learned M, P, S relationships.
منابع مشابه
Approximate Reasoning with Fuzzy-Syllogistic Systems
The well known Aristotelian syllogistic system consists of 256 moods. We have found earlier that 136 moods are distinct in terms of equal truth ratios that range in τ=[0,1]. The truth ratio of a particular mood is calculated by relating the number of true and false syllogistic cases the mood matches. A mood with truth ratio is a fuzzy-syllogistic mood. The introduction of (n-1) fuzzy existentia...
متن کاملGenerating Ontologies from Relational Data with Fuzzy-Syllogistic Reasoning
Existing standards for crisp description logics facilitate information exchange between systems that reason with crisp ontologies. Applications with probabilistic or possibilistic extensions of ontologies and reasoners promise to capture more information, because they can deal with more uncertainties or vagueness of information. However, since there are no standards for either extension, inform...
متن کاملSyllogistic Reasoning as a Basis for Combination of Evidence in Expert Systems
In the presence of uncertainty, computation of the certainty factor of a hypothesis requires, in general, the availability of rules for combining evidence under chaining, dis-junction and conjunction. The method described in this paper is based on the use of what may be viewed as a generalization of syllogistic reasoning in classical logic-a generalization in which numerical or, more generally,...
متن کاملOn the analysis of set-based fuzzy quantified reasoning using classical syllogistics
Syllogism is a type of deductive reasoning involving quantified statements. The syllogistic reasoning scheme in the classical Aristotelian framework involves three crisp term sets and four linguistic quantifiers, for which the main support is the linguistic properties of the quantifiers. A number of fuzzy approaches for defining an approximate syllogism have been proposed for which the main sup...
متن کاملA Fuzzy Syllogistic Reasoning Schema for Generalized Quantifiers
In this paper, a new approximate syllogistic reasoning schema is described that expands some of the approaches expounded in the literature into two ways: (i) a number of different types of quantifiers (logical, absolute, proportional, comparative and exception) taken from Theory of Generalized Quantifiers and similarity quantifiers, taken from statistics, are considered and (ii) any number of p...
متن کامل