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...

The aim of this paper is to provide a Routley-Meyer semantics for Ackermann’s logics of “strenge Implikation” Π′ and Π′′. Besides the Disjunctive Syllogism, this semantics validates the rules Necessitation and Assertion. Strong completeness theorems for Π′ and Π′′ are proved. A brief discussion on Π′, Π′′ and paraconsistency is included.

B.K.Matilal, and earlier J.F.Staal, have suggested a reading of the ‘Nyāya five limb schema’ (also sometimes referred to as the Indian Schema or Hindu Syllogism) from Gotama’s Nyāya-Sūtra in terms of a binary occurrence relation. In this paper we provide a rational justification of a version of this reading as Analogical Reasoning within the framework of Polyadic Pure Inductive Logic.

Alongside theoretical logic, which systematises the proof schemata of theoretical truths, one can systematise the schemata of problem-solving, e.g. those of geometric construction problems. Then, corresponding to the principle of the syllogism, we find for example, the following principle: If we can reduce the solution of b to that of a, and reduce the solution of c to that of b, then we can al...