Knowing Whether
Knowing whether a proposition is true means knowing that it is true or knowing that it is false. In this paper, we study logics with a modal operator Kw for knowing whether but without a modal operator K for knowing that. This logic is not a normal modal logic, because we do not have Kw (phi -> psi) -> (Kw phi -> Kw psi). Knowing whether logic cannot define many common frame properties, and its expressive power less than that of basic modal logic over classes of models without reflexivity. These features make axiomatizing knowing whether logics non-trivial. We axiomatize knowing whether logic over various frame classes. We also present an extension of knowing whether logic with public announcement operators and we give corresponding reduction axioms for that. We compare our work in detail to two recent similar proposals.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Beyond knowing that: a new generation of epistemic logics
Epistemic logic has become a major field of philosophical logic ever since the groundbreaking work by Hintikka (1962). Despite its various successful applications in theoretical computer science, AI, and game theory, the…
Survey"Knowing value" logic as a normal modal logic
Recent years witness a growing interest in nonstandard epistemic logics of "knowing whether", "knowing what", "knowing how", and so on. These logics are usually not normal, i.e., the standard axioms and reasoning rules f…
NegationA New Modal Framework for Epistemic Logic
Recent years witnessed a growing interest in non-standard epistemic logics of knowing whether, knowing how, knowing what, knowing why and so on. The new epistemic modalities introduced in those logics all share, in their…
Semiparametric Efficiency Gains From Parametric Restrictions on Propensity Scores
We explore how much knowing a parametric restriction on propensity scores improves semiparametric efficiency bounds in the potential outcome framework. For stratified propensity scores, considered as a parametric model, …
From Knowing to Acting: Benchmarking Self-Awareness Capability of LLM Agents
The integration of external tools has transitioned LLM agents from passive responders to autonomous systems. However, current benchmarks prioritize execution success, neglecting self-awareness capability, the ability to …