Phased Labeled Logics of Conditional Goals

Abstract

In this paper we introduce phased labeled logics of conditional goals. Labels are used to impose restrictions on the proof theory of the logic. The restriction discussed in this paper is that a proof rule can be blocked in a derivation due to the fact that another proof rule has been applied earlier in the derivation. We call a set of proof rules that can be applied in any order a phase in the proof theory. We propose a one-phase logic of goals containing four proof rules, and we show that it is equivalent to a four-phase logic of goals in which each phase contains exactly one proof rule. The proof theory of the four-phase logic of goals is much more effcient, because other orderings no longer have to be considered.KeywordsInference RuleConsistency CheckProof TheoryDeontic LogicDerivation StepThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.