Constructive Aspects of Gleason's Theorem and Unbounded Operators

Following a brief outline of the contrast between classical mathematics and constructive mathematics--mathematics with intuitionistic logic--I sketch Richman's proof of Gleason's Theorem. I then discuss the First Main Theorem of Pour-El and Richards. In particular, I focus on the wild claim that the First Main Theorem establishes the impossibility of a constructive theory of unbounded operators.

Mathematics behind Ceteris Paribus Preference Logic

The modal logic for ceteris paribus preference logic raises interesting mathematical questions. In this talk, we first discuss the completeness of baisc and ceteris paribus logic. We then take a more general standpoint and investigate how ceteris paribus logic is related to basic and infinitary modal logic. We finally investigate its expressive power and compare it to PDL and the mu-calculus.

Parameterization of Monadic Constraints

A logical formula F(X,P) can be treated as an equation to be satisfied by the solutions X_0(P) with the expressions P as parameters for the expression X (if there is such solutions). In "Parameterizing Models of Propositional Calculus Formulas," J.McCarthy takes up this problem from a slightly different angle, i.e. the parameterization of the models of formulas and gives the general solutions in propositional logic. He suggests a further investigation on the parameterization problem for other logics. In this talk, I will investigate the general solutions for the formulas in monadic first-order predicate logic.