We extend the language of the classical syllogisms with the sentenceforms “At most 1 p is a q” and “More than 1 p is a q”. We show that the resulting logic does not admit a finite set of syllogism-like rules whose associated derivation relation is sound and complete, even when reductio ad absurdum is allowed.

Although Artificial Intelligence (AI) and Machine Learning (ML) are attracting a lot of scientific engineering attention nowadays, nothing up to now has been achieved reach the level building machines that possess human-like intelligence. Though, community continuously claims several problems solved using AI or ML. Here, it is argued engineers not being able build intelligent machines, implying...

This paper provides a review of Rhetoric and the Rule of Law, by Neil MacCormick, focussing on the role of logic in legal reasoning. In particular it considers the connection between syllogism, formal methods and rhetoric, and it distinguishes various aspects of legal defeasibility.

Contemporary students of logic tend to think of the logic of the connectives as the most basic area of the subject, which can then be extended with a logic of quantifiers. Historically, however, the logic of the quantifiers, in the form of the Aristotelian theory of the syllogism, came first. Truth conditions for negation, conjunction, and disjunction were well understood in ancient times, thou...

Based on the syllogism of formal logic and triangulation theory of algebraic topology, a new method of knowledge representation with 2-simplex called simplex representation is given in this paper. To show differences, the method is compared with others. The simplex representation has special characteristics in representation abilities, expression ability, and representation modality. General Te...