aristotle took per impossibile as a form of hypothetical syllogism which was composed of a syllogistic and a non-syllogistic part. but he didn’t express the relation between these two parts clearly. alexander of aphrodisias and philoponus didn’t add any specific comments to aristotle’s view. al-farabi believed that per impossible includes three deductions: two categorical syllogisms and one exc...

Aristotle was the founder of modal logic. In his Prior Analytics, he developed a complex system of modal syllogistic. While influential, this system has been disputed since antiquity and is today widely regarded as incoherent or inconsistent. In view of this, Aristotle’s Modal Syllogistic explores the prospects for understanding the modal syllogistic as a coherent and consistent system of modal...

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...

In [1] Chapter IV Lukasiewicz presents a system of syllogistic which is an extension of Aristotle’s ordinary syllogistic. In spite of this difference Lukasiewicz speaks about it, as do we, as the Aristotelian system. One of the well-known interpretation of syllogistic is Leibnitz’s interpretation described in [1] (pp. 126–129). Syllogistic formulas are interpreted there in an arithmetical manne...

In this paper, we deal with a calculus system SLCD (Syllogistic Logic with Carroll Diagrams), which gives a formal approach to logical reasoning with diagrams, for representations of the fundamental Aristotelian categorical propositions and show that they are closed under the syllogistic criterion of inference which is the deletion of middle term. Therefore, it is implemented to let the formali...

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 After predicate logic had superseded syllogisms in the 19th century, interest on the syllogistic system vanished.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 syllogist...

Ever since Łukasiewicz, it has been opinio communis that Aristotle’s modal syllogistic is incomprehensible due to its many faults and inconsistencies, and that there is no hope of finding a single consistent formal model for it. The aim of this paper is to disprove these claims by giving such a model. My main points shall be, first, that Aristotle’s syllogistic is a pure term logic that does no...

The numerical syllogistic is the extension of the traditional syllogistic with numerical quantifiers of the forms at least C and at most C. It is known that, for the traditional syllogistic, a finite collection of rules, similar in spirit to the classical syllogisms, constitutes a sound and complete proof-system. The question arises as to whether such a proof system exists for the numerical syl...

We introduce ologisms. They generate from ologs by extending their logical expressivity, from the possibility of considering constraints of equational nature only to the possibility of considering constraints of syllogistic nature, in addition. This is obtained by taking advantage of the peculiar features of an original diagrammatic logical calculus for the syllogistic, that make it well-behave...

This paper provides sound and complete logical systems for several fragments of English which go beyond syllogistic logic in that they use verbs as well as other limited syntactic material: universally and existentially quantified noun phrases, building on the work of Nishihara, Morita, and Iwata [7]; complemented noun phrases, following our [6]; and noun phrases which might contain relative cl...