Conditionals for representing implicational and causal knowledge

Abstract

This thesis proposes a model-theoretic approach to address two foundational issues: the semantic conception of indicative conditionals, and that of causation. For many years both issues have remained a tangled series of open problems that attracted great efforts and heated debates among logicians and analytic philosophers, and it is no surprise that these open problems are very fundamental challenges for Artificial Intelligence. The solution proposed in this thesis includes two formal theories introduced in separate chapters. The first theory presents a logic that has a type of conditional for which the exact truth condition is defined, and we argue that using such conditionals enables the appropriate representation of indicative conditionals, or, more assertively, they are indicative conditionals. The second theory is an extension of the first one, where another type of conditional is defined to capture a unified notion of both general causation and specific actual causation. Both theories provide the semantic constructions that realise the desirable properties for representing and reasoning with implicational and causal knowledge without the traditional dilemma of sacrificing some other desirable properties for a formal logic. The Tarskian notion of entailment is preserved in the model theory. Some of these properties are expressed as theorems with proofs provided; other properties are shown by using the semantics to model a series of scenarios in the benchmark examples where we analyse how the difficulties for traditional approaches are resolved in this approach. The logical tools and fundamental claims resulting from this pair of semantic theories may bring a fresh viewpoint or even a general solution to the open problems mentioned above, and contribute to laying a better foundation for the formalisation of commonsense reasoning.