Frege and saving substitution

Substitution Frege and extended Frege proof systems in non-classical logics

We investigate the substitution Frege (SF ) proof system and its relationship to extended Frege (EF ) in the context of modal and superintuitionistic (si) propositional logics. We show that EF is p-equivalent to tree-like SF , and we develop a “normal form” for SF proofs. We establish connections between SF for a logic L, and EF for certain bimodal expansions of L. We then turn attention to spe...

On the substitution between saving and prevention

This work makes a joint analysis of prevention and saving decisions. First we determine the optimal levels of the two variables and we analyze substitution between them. Second we provide some comparative statics results in order to determine the effects on optimal saving and prevention of changes in exogenous present and future wealth and in possible future loss. Finally we introduce insurance...

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