Extending and Automating Basic Probability Theory with Propositional Computability Logic
Classical probability theory is formulated using sets. In this paper, we extend classical probability theory with propositional computability logic. Unlike other formalisms, computability logic is built on the notion of events/games, which is central to probability theory. The probability theory based on CoL is therefore useful for {\it automating} uncertainty reasoning. We describe some basic properties of this new probability theory. We also discuss a novel isomorphism between the set operations and computability logic operations.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
From Propositional Logic to Plausible Reasoning: A Uniqueness Theorem
We consider the question of extending propositional logic to a logic of plausible reasoning, and posit four requirements that any such extension should satisfy. Each is a requirement that some property of classical propo…
In principle determination of generic priors
Probability theory as extended logic is completed such that essentially any probability may be determined. This is done by considering propositional logic (as opposed to predicate logic) as syntactically suffcient and im…
Learning algorithms versus automatability of Frege systems
We connect learning algorithms and algorithms automating proof search in propositional proof systems: for every sufficiently strong, well-behaved propositional proof system $P$, we prove that the following statements are…
Propositional Abduction via Only-Knowing: A Non-Monotonic Approach
The paper introduces a basic logic of knowledge and abduction by extending Levesque logic of only-knowing with an abduction modal operator defined via the combination of basic epistemic concepts. The upshot is an alterna…
Reasoning about Expectation
Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics …