Related papers: Reasoning About Knowledge of Unawareness Revisited
This paper adds counterfactuals to the framework of knowledge-based programs of Fagin, Halpern, Moses, and Vardi. The use of counterfactuals is illustrated by designing a protocol in which an agent stops sending messages once it knows that…
Epistemic logics model how agents reason about their beliefs and the beliefs of other agents. Existing logics typically assume the ability of agents to reason perfectly about propositions of unbounded modal depth. We present DBEL, an…
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 technical…
We consider a family U of finite universes. The second order quantifier Q_R, means for each u in U quantifying over a set of n(R)-place relations isomorphic to a given relation. We define a natural partial order on such quantifiers called…
In this paper we study the notion of knowledge from the positions of universal algebra and algebraic logic. We consider first order knowledge which is based on first order logic. We define categories of knowledge and knowledge bases. These…
We give a new elementary proof of the main theorem of [Fef12]: Quantifiers implicitly definable in pure second-order logic equipped with Henkin semantics implies are (explicitly) definable in first-order logic.
We provide a logical framework in which a resource-bounded agent can be seen to perform approximations of probabilistic reasoning. Our main results read as follows. First we identify the conditions under which propositional probability…
While a large body of work has scrutinized the meaning of conditional sentences, considerably less attention has been paid to formal models of their pragmatic use and interpretation. Here, we take a probabilistic approach to pragmatic…
We discuss views about whether the universe can be rationally comprehended, starting with Plato, then Leibniz, and then the views of some distinguished scientists of the previous century. Based on this, we defend the thesis that…
Explainable systems expose information about why certain observed effects are happening to the agents interacting with them. We argue that this constitutes a positive flow of information that needs to be specified, verified, and balanced…
Analogous to G\"odel's incompleteness theorems is a theorem in physics to the effect that the set of explanations of given evidence is uncountably infinite. An implication of this theorem is that contact between theory and experiment…
Dynamic epistemic logics which model abilities of agents to make various announcements and influence each other's knowledge have been studied extensively in recent years. Two notable examples of such logics are Group Announcement Logic and…
The compactness theorem for a logic states, roughly, that the satisfiability of a set of well-formed formulas can be determined from the satisfiability of its finite subsets, and vice versa. Usually, proofs of this theorem depend on the…
A definition of what counts as an explanation of mathematical statement, and when one explanation is better than another, is given. Since all mathematical facts must be true in all causal models, and hence known by an agent, mathematical…
We formalize two independent computational limitations that constrain algorithmic intelligence: formal incompleteness and dynamical unpredictability. The former limits the deductive power of consistent reasoning systems while the latter…
We explore uncertainty quantification in large language models (LLMs), with the goal to identify when uncertainty in responses given a query is large. We simultaneously consider both epistemic and aleatoric uncertainties, where the former…
Coalition Logic is primarily concerned with what coalitions can achieve, whereas what coalitions cannot achieve -- their \emph{inability} -- has received comparatively little explicit attention. This asymmetry matters in artificial…
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 semantics, the…
In this paper we formulate the problem of inference under incomplete information in very general terms. This includes modelling the process responsible for the incompleteness, which we call the incompleteness process. We allow the process…
Propositional team logic is the propositional analog to first-order team logic. Non-classical atoms of dependence, independence, inclusion, exclusion and anonymity can be expressed in it, but for all atoms except dependence only exponential…