(Pure) logic out of probability

Abstract

Logic and Probability are seen today as independent fields, but they share a considerable common ground, which historically underlies both disciplines and has prompted Reichenbach, Carnap or Popper to consider connection-building treatments of Logic and Probability as desirable. In this spirit we delineate a logic based on an additive non-functional truth valuation which, though technically indistinguishable from (axiomatic) Probability, can however be "decontaminated" from parasitical probabilistic readings (such as "event", "probability" or "conditioning") and be given instead a logical reading (in terms of "sentence", "truth" or "relativity"). The resulting assertion-based sentential calculus becomes a very natural extension of ordinary two-valued reasoning. The text of the paper corresponds to the author's invited contribution to the Workshop on "Aspects of mechanizing inference", held in Naples Oct. 30 - Nov. 2, 1995.

Logic and Probability are seen today as independent fields, but they share a considerable common ground, which historically underlies both disciplines and has prompted Reichenbach, Carnap or Popper to consider connection-building treatments of Logic and Probability as desirable. In this spirit we delineate a logic based on an additive non-functional truth valuation which, though technically indistinguishable from (axiomatic) Probability, can however be "decontaminated" from parasitical probabilistic readings (such as "event", "probability" or "conditioning") and be given instead a logical reading (in terms of "sentence", "truth" or "relativity"). The resulting assertion-based sentential calculus becomes a very natural extension of ordinary two-valued reasoning.