A Probabilistic Propositional Logic System Is an Event Semantics for Classical Formal System of Propositional Calculus

摘要

The well formed formulas (wffs) in classical formal system of propositional calculus (CPC) are only some formal symbols, whose meanings are given by an interpretation. A probabilistic logic system, based on a probabilistic space, is an event semantics for CPC, in which set operations are the semantic interpretations for connectives, event functions are the semantic interpretations for wffs, the event (set) inclusion {is contained in} is the semantic interpretation for tautological implication, and the event equality = is the semantic interpretation for tautological equivalence. CPC is applicable to probabilistic propositions completely. Event calculus instead of truth value (probability) calculus can be performed in CPC because there aren't truth value functions (operators) to interpret all connectives correctly.