Vitaliy Dolgorukov

We present a static (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textsf{EL}_{\textsf{bc}}$$\end{document}) and dynamic (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textsf{DEL}_{\textsf{bc}}$$\end{document}) epistemic logic for budget-constrained agents, in which an agent can obtain some information in exchange for budget resources. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textsf{EL}_{\textsf{bc}}$$\end{document} extends a standard multi-agent epistemic logic with expressions concerning agent’s budgets and formulas’ costs. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textsf{DEL}_{\textsf{bc}}$$\end{document} extends \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textsf{EL}_{\textsf{bc}}$$\end{document} with dynamic modality “\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$[?_i A]\varphi $$\end{document}” which reads as “\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi $$\end{document} holds after i’s question whether a propositional formula A is true”. In this paper we provide a sound and complete axiomatization for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textsf{EL}_{\textsf{bc}}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textsf{DEL}_{\textsf{bc}}$$\end{document} and show that both logics are decidable.

The paper proposes an epistemic taxonomy of assertives based on a concept of epistemic presuppositions. Epistemic presuppositions are a special kind of pragmatic presuppositions, which describe the structure of hearer’s and speaker’s meta-reasoning. The epistemic taxonomy of assertives is based on the operator of strong common belief (sCB). It is argued that the properties of a strong common belief operator (positive and negative introspection, non-factivity) are relevant for the analysis of pragmatics presuppositions. Also strong common belief operator is used for the explication of gricean epistemic construction: “the Speaker thinks (and would expect the hearer to think that the speaker thinks…”. The assertives’ taxonomy for an utterance φ consists of the following basic types: “1. Non-Literal Utterances” (sCBS,H¬φ) and “2. Literal Utterances” (¬sCBS,H¬φ). Non-Literal Utterances is divided into two groups: “1.1. Conventional Literal Utterances“ (there is a convention such that means ψ in a context c.) and “1.2. Non- Conventional Literal Utterances“ (there no such convention). There are two types of Literal Utterances “2.1. Semantically Trivial Utterances (sCBS,Hφ)” and “2.2. Semantically Non-Trivial Utterances (¬sCBS,Hφ)”. Semantically Trivial Utterances is divided into two parts: “2.1.1. Conventional Semantically Trivial Utterances” (there is a convention such that means ψ in a context c) and “2.1.2. Non-conventional Semantically Trivial Utterances” (there no such convention). Semantically Non-Trivial Utterances is divided into two parts: “2.2.1. Insincere Utterances” BS¬φ and “2.2.2. Sincere Utterances ¬BS¬φ. There are two types of Sincere Utterances “2.2.2.1. Credible Utterances” (BSφ) and “2.2.2.2. Non-credible Utterances”).