Reconciling Aristotle and Frege

Three Logicians: Aristotle, Saccheri, Frege

Relational Exploration - Reconciling Plato and Aristotle

We provide an interactive method for knowledge acquisition combining approaches from description logic and formal concept analysis. Based on present data, hypothetical rules are formulated and checked against a description logic theory. We propose an abstract framework (Logical Domain Exploration) for this kind of exploration technique before presenting a concrete instantiation: Relational Expl...

Propositional Proofs in Frege and Extended Frege Systems (Abstract)

We discuss recent results on the propositional proof complexity of Frege proof systems, including some recently discovered quasipolynomial size proofs for the pigeonhole principle and the Kneser-Lovász theorem. These are closely related to formalizability in bounded arithmetic.

Frege, Contextuality and Compositionality

The name ‘Frege’s principle’ is well known: it is discussed, obeyed or rejected in philosophy, linguistics, logic and computer science (see e.g. [33] and[45]). Surprisingly, two completely different principles which are denoted by that name. In most fields it refers to ‘the principle of compositionality of meaning’: The meaning of a compound expression is a function of the meaning of its parts ...

Frege Systems