Related papers: Knowing Whether
The uniform interpolation property in a given logic can be understood as the definability of propositional quantifiers. We mechanise the computation of these quantifiers and prove correctness in the Coq proof assistant for three modal…
We recently described a formalism for reasoning with if-then rules that re expressed with different levels of firmness [18]. The formalism interprets these rules as extreme conditional probability statements, specifying orders of magnitude…
We study the satisfiability problem for a modal logic expressing knowing-how assertions, which captures an agent's ability to achieve a given goal under the standard semantics based on linear plans. Our main result shows that satisfiability…
Common Knowledge Logic is meant to describe situations of the real world where a group of agents is involved. These agents share knowledge and make strong statements on the knowledge of the other agents (the so called \emph{common…
This work builds upon a well-established research tradition on modal logics of awareness. One of its aims is to export tools and techniques to other areas within modal logic. To this end, we illustrate a number of significant bridges with…
We analyze the informal semantic conception of proof and axiomatize the proof relation and the provability operator. A self referential propositional calculus which admits provable liar type sentences is introduced and proven consistent. We…
Cathoristic logic is a multi-modal logic where negation is replaced by a novel operator allowing the expression of incompatible sentences. We present the syntax and semantics of the logic including complete proof rules, and establish a…
Standard models of multi-agent modal logic do not capture the fact that information is often ambiguous, and may be interpreted in different ways by different agents. We propose a framework that can model this, and consider different…
We look at non-classical negations and their corresponding adjustment connectives from a modal viewpoint, over complete distributive lattices, and apply a very general mechanism in order to offer adequate analytic proof systems to logics…
We introduce a logic for reasoning about evidence that essentially views evidence as a function from prior beliefs (before making an observation) to posterior beliefs (after making the observation). We provide a sound and complete…
I show that probabilities in quantum mechanics are a measure of belief in the presence of human ignorance, just like all other probabilities. The Born interpretation of the square of modulus of the wave function arises from the interaction…
Logical propositions with the fuzzy modality "Probably" are shown to obey an uncertainty principle very similar to that of Quantum Optics. In the case of such propositions, the partial truth values are in fact probabilities. The…
A model of knowledge representation is described in which propositional facts and the relationships among them can be supported by other facts. The set of knowledge which can be supported is called the set of cognitive units, each having…
A natural way to represent beliefs and the process of updating beliefs is presented by Bayesian probability theory, where belief of an agent a in P can be interpreted as a considering that P is more probable than not P. This paper attempts…
We combine the concepts of modal logics and many-valued logics in a general and comprehensive way. Namely, given any finite linearly ordered set of truth values and any set of propositional connectives defined by truth tables, we define the…
Prime implicates and prime implicants have proven relevant to a number of areas of artificial intelligence, most notably abductive reasoning and knowledge compilation. The purpose of this paper is to examine how these notions might be…
In epistemic logic, a way to deal with knowledge-wh is to interpret them as a kind of mention-some knowledge (MS-knowledge). But philosophers and linguists have challenged both the sufficiency and necessity of such an account: some argue…
We present a new system S for handling uncertainty in a quantified modal logic (first-order modal logic). The system is based on both probability theory and proof theory. The system is derived from Chisholm's epistemology. We concretize…
Recent research in extensions of Answer Set Programming has included a renewed interest in the language of Epistemic Specifications, which adds modal operators K ("known") and M ("may be true") to provide for more powerful introspective…
The classical propositional logic is known to be sound and complete with respect to the set semantics that interprets connectives as set operations. The paper extends propositional language by a new binary modality that corresponds to…