Date of Award
Spring 1995
Document Type
Dissertation - Restricted
Degree Name
Doctor of Philosophy (PhD)
Department
Interdisciplinary
First Advisor
Ruitenburg, Wim
Second Advisor
Bankston, Paul
Third Advisor
Jones, Peter
Abstract
Basic Propositional Logic, BPL, was invented by Albert Visser in 1981 [Vi81]. He wanted to interpret implication as formal provability. To protect his system against the liar paradox, modus ponens is weakened. His axiomatization of BPL uses natural deduction (see page 8). In his thesis, Visser proved the completeness of BPL with respect to finite Kripke models. He extended BPL to Formal Propositional Logic, FPL, by adding Lob's Rule, "formula", and continued his studies in that direction. One decade later Wim Ruitenburg [Ru91], considering philosophical criticisms of the intuitionistic interpretation of the logical connectives, reintroduced BPL and a first order extension, BQC...