Common Knowledge of Abstract Groups

• URL: http://arxiv.org/abs/2211.16284v1
• Date: Tue, 29 Nov 2022 15:11:28 GMT
• Title: Common Knowledge of Abstract Groups
• Authors: Merlin Humml, Lutz Schr\"oder
• Abstract summary: AGEL features a common knowledge operator for groups of agents given by concepts in a separate agent logic. We show that AGEL is EXPTIME-complete, with the lower bound established by reduction from standard group epistemic logic. Further results include a finite model property (not enjoyed by the full $mu$-calculus) and a complete axiomatization.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: Epistemic logics typically talk about knowledge of individual agents or groups of explicitly listed agents. Often, however, one wishes to express knowledge of groups of agents specified by a given property, as in `it is common knowledge among economists'. We introduce such a logic of common knowledge, which we term abstract-group epistemic logic (AGEL). That is, AGEL features a common knowledge operator for groups of agents given by concepts in a separate agent logic that we keep generic, with one possible agent logic being ALC. We show that AGEL is EXPTIME-complete, with the lower bound established by reduction from standard group epistemic logic, and the upper bound by a satisfiability-preserving embedding into the full $\mu$-calculus. Further main results include a finite model property (not enjoyed by the full $\mu$-calculus) and a complete axiomatization.

Related papers

• Virtual Group Knowledge and Group Belief in Topological Evidence Models (Extended Version) [41.99844472131922]
  We study notions of (virtual) group knowledge and group belief within multi-agent evidence models.<n>We axiomatize and show the decidability of the logic of "hard" and "soft" group evidence.
  arXiv  Detail & Related papers  (2025-08-29T18:33:54Z)
• Analogical proportions II [0.0]
  Analogical reasoning is the ability to detect parallels between two seemingly distant objects or situations. Analogical proportions are expressions of the form $a$ is to $b$ what $c$ is to $d$'' at the core of analogical reasoning.
  arXiv  Detail & Related papers  (2024-05-22T09:02:12Z)
• A Semantic Approach to Decidability in Epistemic Planning (Extended Version) [72.77805489645604]
  We use a novel semantic approach to achieve decidability. Specifically, we augment the logic of knowledge S5$_n$ and with an interaction axiom called (knowledge) commutativity. We prove that our framework admits a finitary non-fixpoint characterization of common knowledge, which is of independent interest.
  arXiv  Detail & Related papers  (2023-07-28T11:26:26Z)
• A Theory of Bounded Inductive Rationality [0.0]
  We develop a theory of rational decision making that does not assume logical omniscience. We consider agents who repeatedly face decision problems, including ones like betting on digits of pi. We prove that agents that are rational in this sense have other desirable properties.
  arXiv  Detail & Related papers  (2023-07-11T07:13:29Z)
• Modeling Hierarchical Reasoning Chains by Linking Discourse Units and Key Phrases for Reading Comprehension [80.99865844249106]
  We propose a holistic graph network (HGN) which deals with context at both discourse level and word level, as the basis for logical reasoning. Specifically, node-level and type-level relations, which can be interpreted as bridges in the reasoning process, are modeled by a hierarchical interaction mechanism.
  arXiv  Detail & Related papers  (2023-06-21T07:34:27Z)
• Non-deterministic approximation operators: ultimate operators, semi-equilibrium semantics and aggregates (full version) [13.249453757295083]
  We make three further contributions to non-deterministic AFT. We define and study ultimate approximations of non-deterministic operators. We generalize the characterisations of disjunctive logic programs to disjunctive logic programs with aggregates.
  arXiv  Detail & Related papers  (2023-05-18T09:59:12Z)
• The Transformation Logics [58.35574640378678]
  We introduce a new family of temporal logics designed to balance the trade-off between expressivity and complexity. Key feature is the possibility of defining operators of a new kind that we call transformation operators. We show them to yield logics capable of creating hierarchies of increasing expressivity and complexity.
  arXiv  Detail & Related papers  (2023-04-19T13:24:04Z)
• ArT: All-round Thinker for Unsupervised Commonsense Question-Answering [54.068032948300655]
  We propose an approach of All-round Thinker (ArT) by fully taking association during knowledge generating. We evaluate it on three commonsense QA benchmarks: COPA, SocialIQA and SCT.
  arXiv  Detail & Related papers  (2021-12-26T18:06:44Z)
• Modeling and Automating Public Announcement Logic with Relativized Common Knowledge as a Fragment of HOL in LogiKEy [0.0]
  This article presents a semantical embedding for public announcement logic with relativized common knowledge. It enables the first-time automation of this logic with off-the-shelf theorem provers for classical higher-order logic. The work constitutes an important addition to the pluralist LogiKEy knowledge engineering methodology.
  arXiv  Detail & Related papers  (2021-11-02T15:14:52Z)
• Aleatoric Description Logic for Probailistic Reasoning (Long Version) [0.2538209532048866]
  Aleatoric description logic models uncertainty in the world as aleatoric events, by the roll of the dice, where an agent has subjective beliefs about the bias of these dice. This provides a subjective Bayesian description logic, where propositions and relations are assigned probabilities according to what a rational agent would bet. Several computational problems are considered and model-checking and consistency checking algorithms are presented.
  arXiv  Detail & Related papers  (2021-08-30T07:47:36Z)
• Fact-driven Logical Reasoning for Machine Reading Comprehension [82.58857437343974]
  We are motivated to cover both commonsense and temporary knowledge clues hierarchically. Specifically, we propose a general formalism of knowledge units by extracting backbone constituents of the sentence. We then construct a supergraph on top of the fact units, allowing for the benefit of sentence-level (relations among fact groups) and entity-level interactions.
  arXiv  Detail & Related papers  (2021-05-21T13:11:13Z)
• Foundations of Reasoning with Uncertainty via Real-valued Logics [70.43924776071616]
  We give a sound and strongly complete axiomatization that can be parametrized to cover essentially every real-valued logic. Our class of sentences are very rich, and each describes a set of possible real values for a collection of formulas of the real-valued logic.
  arXiv  Detail & Related papers  (2020-08-06T02:13:11Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.