Reasoning about general preference relations

Preference relations are at the heart of many fundamental concepts in artificial intelligence, ranging from utility comparisons, to defeat among strategies and relative plausibility states, just mention a few. Reasoning about such has been object extensive research wealth formalisms exist express reason them. One formalism is conditional logic, which focuses on reasoning “best” alternatives according given preference relation. A alternative normally interpreted as an that either maximal (no other preferred it) or optimal (it least all alternatives). And relation assumed satisfy strong requirements (typically transitivity some kind well-foundedness assumption). Here, we generalize this existing literature two ways. Firstly, addition maximality optimality, consider interpretations “best”, call unmatchedness acceptability. Secondly, do not inherently require any constraints. Instead, allow combination transitivity, totality anti-symmetry. This allows us model wide range situations, including cases where lack constraints stems modeled agent being irrational (for example, might have preferences neither transitive nor total anti-symmetric) interaction perfectly rational agents game be anti-symmetric but transitive). For each interpretation (maximal, optimal, unmatched acceptable) (transitivity, and/or anti-symmetry), study sets valid inferences. Specifically, one case introduce sound strongly complete axiomatization, remaining show no axiomatization exists.