Classical Logic—Basic Tableaus

Abstract

Several varieties of proof procedures have been developed for firstorder classical logic. Among them the semantic tableau procedure has a considerable attraction, [Smu68, Fit96] . It is intuitive, close to the intended semantics, and is automatable. For higher-order classical logic, semantic tableaus are not as often seen—most treatments in the literature are axiomatic. Among the notable exceptions are [ToI75, Smi93, Koh95, GilOl] . In fact, semantic tableaus retain much of their first-order ability to charm, and they are what I present here. Automatability becomes more problematic, however, for reasons that will become clear as we proceed. Consequently the presentation should be thought of as meant for human use, and intelligence in the construction of proofs is expected.