ECL₃: Epistemic Causal Logic — Paper I: Core Logic, Semantics, and Completeness

Abstract

We introduce ECL3 (Epistemic Causal Logic), a three-valued formal logic extending Łukasiewicz L3 with an observability predicate Obs and a causal operator Cause. The system distinguishes truth (what is the case), observability (whether it can be known), and causal accessibility (what brings about observability) as independent but interacting semantic dimensions. The paper presents: (1) a two-level architecture separating object language from metalanguage via explicit bridge rules; (2) formal transition semantics with three primitive actions replacing operational notation; (3) a Kripke-style completeness proof including a three-valued Lindenbaum lemma, canonical model construction, five auxiliary lemmas, and a full inductive Truth Lemma; (4) σ-relative completeness with compositional stability of RF2. The system is proven sound and complete. Core theorems include the formal isolation of true-but-unobservable propositions and the derivation of RF2 from axiom C2 and bridge rule BR1.