Is Mathematical Logic Really Necessary in Teaching Mathematical Proofs?

The Role of Logic in the Validation of Mathematical Proofs

What is mathematical fuzzy logic

The paper comments on the development and present state of fuzzy logic as a kind (branch) of mathematical logic. It is meant just as a contribution to the discussion on what fuzzy logic is, not as a systematic presentation of mathematical fuzzy logic. © 2005 Elsevier B.V. All rights reserved.

MENON: automating a Socratic teaching model for mathematical proofs

Adaptive teaching strategies that take the needs of different learners into account are a prerequisite for successful intelligent tutoring systems. They should ideally incorporate elements of all facets of teaching that together are responsible for learning. One such facet is natural language tutorial dialogue, which is crucial to the application of teaching strategies by human teachers. Althou...

Mathematical Logic

We prove that every homogeneously Souslin set is coanalytic provided that either (a) 0long does not exist, or else (b) V = K , where K is the core model below a μ-measurable cardinal. 1. Homogeneously Souslin sets In this paper we shall deal with homogeneously Souslin sets of reals, or rather with sets of reals which admit an ω-closed embedding normal form. Definition 1.1. (Cf. [4, p. 92].) Let...

Mathematical Logic

When we cut a multiplicative proof-net of linear logic in two parts we get two modules with a certain border. We call pretype of a module the set of partitions over its border induced by Danos-Regnier switchings. The type of a module is then defined as the double orthogonal of its pretype. This is an optimal notion describing the behaviour of a module: two modules behave in the same way precise...