Related papers: Models for the common knowledge logic
We define a family of intuitionistic non-normal modal logics; they can bee seen as intuitionistic counterparts of classical ones. We first consider monomodal logics, which contain only one between Necessity and Possibility. We then consider…
Given a class C of finite Kripke frames, we consider the uniform distribution on the frames from C with n states. A formula is almost surely valid in C if the probability that it is valid in a random C-frame with n states tends to 1 as n…
Let $\Theta$ be a variety of algebras, $(H, \Psi, f)$ be a model, where $H$ is an algebra from $\Theta$, $\Psi$ is a set of relation symbols $\varphi$, $f$ is an interpretation of all $\varphi$ in $H$. Let $X^0$ be an infinite set of…
In this paper, we propose a single-agent modal logic framework for reasoning about goal-direct "knowing how" based on ideas from linguistics, philosophy, modal logic and automated planning. We first define a modal language to express "I…
We study model and frame definability of various modal logics. Let ML(A+) denote the fragment of modal logic extended with the universal modality in which the universal modality occurs only positively. We show that a class of Kripke models…
Common knowledge/belief in rationality is the traditional standard assumption in analysing interaction among agents. This paper proposes a graph-based language for capturing significantly more complicated structures of higher-order beliefs…
The semantic framework for the modal logic of knowledge due to Halpern and Moses provides a way to ascribe knowledge to agents in distributed and multi-agent systems. In this paper we study two special cases of this framework: full systems…
In this paper, we provide simplified semantics for the logic K45(G), i.e. the many-valued Godel counterpart of the classical modal logic K45. More precisely, we characterize K45(G) as the set of valid formulae of the class of possibilistic…
Machine common sense remains a broad, potentially unbounded problem in artificial intelligence (AI). There is a wide range of strategies that can be employed to make progress on this challenge. This article deals with the aspects of…
This paper investigates the contingency of logic within the framework of possible world semantics. Possible world semantics captures the meaning of necessitation, i.e., a statement is necessarily true if it holds in all possible worlds.…
This paper introduces the notion of `commonly knowing whether', a non-standard version of standard common knowledge which is defined on the basis of `knowing whether', instead of standard `knowing that'. After giving five possible…
We present the detailed account of the quantum(-like) viewpoint to common knowledge. The Binmore-Brandenburger operator approach to the notion of common knowledge is extended to the quantum case. We develop a special quantum(-like) model of…
We propose a modal study of the notion of bisimulation. Our contribution is threefold. First, we extend the basic modal language with a new modality $\nbi$, whose intended meaning is universal quantification over all states that are…
The premise of the Multi-disciplinary Conference on Reinforcement Learning and Decision Making is that multiple disciplines share an interest in goal-directed decision making over time. The idea of this paper is to sharpen and deepen this…
Commonsense reasoning aims to incorporate sets of commonsense facts, retrieved from Commonsense Knowledge Graphs (CKG), to draw conclusion about ordinary situations. The dynamic nature of commonsense knowledge postulates models capable of…
We propose communication pattern logic. A communication pattern describes how processes or agents inform each other, independently of the information content. The full-information protocol in distributed computing is the special case…
Commonsense knowledge-graphs (CKGs) are important resources towards building machines that can 'reason' on text or environmental inputs and make inferences beyond perception. While current CKGs encode world knowledge for a large number of…
A famous result, conjectured by G\"odel in 1932 and proved by McKinsey and Tarski in 1948, says that $\varphi$ is a theorem of intuitionistic propositional logic IPC iff its G\"odel-translation $\varphi'$ is a theorem of modal logic S4. In…
Given a class $\mathcal C$ of models, a binary relation ${\mathcal R}$ between models, and a model-theoretic language $L$, we consider the modal logic and the modal algebra of the theory of $\mathcal C$ in $L$ where the modal operator is…
We study public announcement operators in the context of standard G\"odel modal logic as introduced by Caicedo and Rodriguez. Over that base logic, admitting a natural semantics over [0,1]-valued generalizations of modal Kripke models, we…