Logics for Knowability

Public Announcement ◽

Public Announcement Logic ◽

Multi Agent ◽

Soundness And Completeness

In this paper, we propose three knowability logics LK, LK−, and LK=. In the single-agent case, LK is equally expressive as arbitrary public announcement logic APAL and public announcement logic PAL, whereas in the multi-agent case, LK is more expressive than PAL. In contrast, both LK− and LK= are equally expressive as classical propositional logic PL. We present the axiomatizations of the three knowability logics and show their soundness and completeness. We show that all three knowability logics possess the properties of Church-Rosser and McKinsey. Although LK is undecidable when at least three agents are involved, LK− and LK= are both decidable.

Deduction in Non-Fregean Propositional Logic SCI

Axioms ◽

10.3390/axioms8040115 ◽

2019 ◽

Vol 8 (4) ◽

pp. 115 ◽

Author(s):

Joanna Golińska-Pilarek ◽

Magdalena Welle

Keyword(s):

Propositional Logic ◽

Sequent Calculus ◽

Tableau System ◽

Soundness And Completeness

We study deduction systems for the weakest, extensional and two-valued non-Fregean propositional logic SCI . The language of SCI is obtained by expanding the language of classical propositional logic with a new binary connective ≡ that expresses the identity of two statements; that is, it connects two statements and forms a new one, which is true whenever the semantic correlates of the arguments are the same. On the formal side, SCI is an extension of classical propositional logic with axioms characterizing the identity connective, postulating that identity must be an equivalence and obey an extensionality principle. First, we present and discuss two types of systems for SCI known from the literature, namely sequent calculus and a dual tableau-like system. Then, we present a new dual tableau system for SCI and prove its soundness and completeness. Finally, we discuss and compare the systems presented in the paper.

Update Semantics in Communicated Information System

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.403-408.1460 ◽

2011 ◽

Vol 403-408 ◽

pp. 1460-1465

Author(s):

Guang Ming Chen ◽

Xiao Wu Li

Keyword(s):

Information Systems ◽

Propositional Logic ◽

General Purpose ◽

Main Task ◽

Information Communication ◽

Update Semantics ◽

Essential Form ◽

Soundness And Completeness ◽

Multi Agents

An approach, which is called Communicated Information Systems, is introduced to describe the information available in a number of agents and specify the information communication among the agents. The systems are extensions of classical propositional logic in multi-agents context, providing with us a way by which not only the agent’s own information, but the information from other agents may be applied to agent’s reasoning as well. Communication rules, which are defined in the most essential form, can be regarded as the base to characterize some interesting cognitive proporties of agents. Since the corresponding communication rules can be chosen for different applications, the approach is general purpose one. The other main task is that the soundness and completeness of the Communicated Information Systems for the update semantics have been proved in the paper.

Hybrid Deduction–Refutation Systems

Axioms ◽

10.3390/axioms8040118 ◽

2019 ◽

Vol 8 (4) ◽

pp. 118 ◽

Author(s):

Valentin Goranko

Keyword(s):

Propositional Logic ◽

Proof Theory ◽

Natural Deduction ◽

Basic Theory ◽

Logical System ◽

Deductive Systems ◽

Refutation Systems ◽

Soundness And Completeness

Hybrid deduction–refutation systems are deductive systems intended to derive both valid and non-valid, i.e., semantically refutable, formulae of a given logical system, by employing together separate derivability operators for each of these and combining ‘hybrid derivation rules’ that involve both deduction and refutation. The goal of this paper is to develop a basic theory and ‘meta-proof’ theory of hybrid deduction–refutation systems. I then illustrate the concept on a hybrid derivation system of natural deduction for classical propositional logic, for which I show soundness and completeness for both deductions and refutations.

A cut-free labelled sequent calculus for dynamic epistemic logic

Journal of Logic and Computation ◽

10.1093/logcom/exaa014 ◽

2020 ◽

Vol 30 (1) ◽

pp. 321-348

Author(s):

Shoshin Nomura ◽

Hiroakira Ono ◽

Katsuhiko Sano

Keyword(s):

Modal Logic ◽

Epistemic Logic ◽

Sequent Calculus ◽

Dynamic Epistemic Logic ◽

Kripke Semantics ◽

Cut Rule ◽

Public Announcement ◽

Public Announcement Logic ◽

Soundness And Completeness ◽

Labelled Sequent Calculus

Abstract Dynamic epistemic logic is a logic that is aimed at formally expressing how a person’s knowledge changes. We provide a cut-free labelled sequent calculus ($\textbf{GDEL}$) on the background of existing studies of Hilbert-style axiomatization $\textbf{HDEL}$ of dynamic epistemic logic and labelled calculi for public announcement logic. We first show that the $cut$ rule is admissible in $\textbf{GDEL}$ and show that $\textbf{GDEL}$ is sound and complete for Kripke semantics. Moreover, we show that the basis of $\textbf{GDEL}$ is extended from modal logic K to other familiar modal logics including S5 with keeping the admissibility of cut, soundness and completeness.

DYNAMIC CONSEQUENCE AND PUBLIC ANNOUNCEMENT

The Review of Symbolic Logic ◽

10.1017/s1755020313000294 ◽

2013 ◽

Vol 6 (4) ◽

pp. 659-679 ◽

Author(s):

ANDRÉS CORDÓN FRANCO ◽

HANS VAN DITMARSCH ◽

ANGEL NEPOMUCENO

Keyword(s):

Common Knowledge ◽

Consequence Relations ◽

Multi Agent Systems ◽

Consequence Relation ◽

Agent Systems ◽

Public Announcement ◽

Public Announcement Logic ◽

Multi Agent ◽

Image Position ◽

Open Question

AbstractIn van Benthem (2008), van Benthem proposes a dynamic consequence relation defined as ${\psi _1}, \ldots ,{\psi _n}{ \models ^d}\phi \,{\rm{iff}}{ \models ^{pa}}[{\psi _1}] \ldots [{\psi _n}]\phi ,$ where the latter denotes consequence in public announcement logic, a dynamic epistemic logic. In this paper we investigate the structural properties of a conditional dynamic consequence relation $\models _{\rm{\Gamma }}^d$ extending van Benthem’s proposal. It takes into account a set of background conditions Γ, inspired by Makinson (2003) wherein Makinson calls this reasoning ‘modulo’ a set Γ. In the presence of common knowledge, conditional dynamic consequence is definable from (unconditional) dynamic consequence. An open question is whether dynamic consequence is compact. We further investigate a dynamic consequence relation for soft instead of hard announcements. Surprisingly, it shares many properties with (hard) dynamic consequence. Dynamic consequence relations provide a novel perspective on reasoning about protocols in multi-agent systems.

Introducing k-lingo: a k-depth Bounded Version of ASP System Clingo

10.24963/kr.2021/65 ◽

2021 ◽

Author(s):

Fabio Aurelio D'Asaro ◽

Paolo Baldi ◽

Giuseppe Primiero

Keyword(s):

Computational Complexity ◽

Propositional Logic ◽

Multi Agent Systems ◽

Rational Agents ◽

Agent Systems ◽

Multi Agent ◽

Future Work ◽

Limited Depth

Depth-Bounded Boolean Logics (DBBL for short) are well-understood frameworks to model rational agents equipped with limited deductive capabilities. These Logics use a parameter k>=0 to limit the amount of virtual information, i.e., the information that the agent may temporarily assume throughout the deductive process. This restriction brings several advantageous properties over classical Propositional Logic, including polynomial decision procedures for deducibility and refutability. Inspired by DBBL, we propose a limited-depth version of the popular ASP system \clingo, tentatively dubbed k-lingo after the bound k on virtual information. We illustrate the connection between DBBL and ASP through examples involving both proof-theoretical and implementative aspects. The paper concludes with some comments on future work, which include a computational complexity characterization of the system, applications to multi-agent systems and feasible approximations of probability functions.

On Reasoning about Access to Knowledge

10.29007/z15j ◽

2020 ◽

Author(s):

Yakoub Salhi

Keyword(s):

Crucial Role ◽

Propositional Logic ◽

Basic Problem ◽

Multi Agent Systems ◽

Inference Process ◽

Agent Systems ◽

Multi Agent ◽

Classical Inference ◽

Access To Knowledge

Controlling access to knowledge plays a crucial role in many multi-agent systems. In- deed, it is related to different central aspects in interactions among agents such as privacy, security, and cooperation. In this paper, we propose a framework for dealing with access to knowledge that is based on the inference process in classical propositional logic: an agent has access to every piece of knowledge that can be derived from the available knowledge using the classical inference process. We first introduce a basic problem in which an agent has to hide pieces of knowledge, and we show that this problem can be solved through the computation of maximal consistent subsets. In the same way, we also propose a coun- terpart of the previous problem in which an agent has to share pieces of knowledge, and we show that this problem can be solved through the computation of minimal inconsis- tent subsets. Then, we propose a generalization of the previous problem where an agent has to share pieces of knowledge and hide at the same time others. In this context, we introduce several concepts that allow capturing interesting aspects. Finally, we propose a weight-based approach by associating integers with the pieces of knowledge that have to be shared or hidden.

Multi-Agent Reinforcement Learning: A Review of Challenges and Applications

Applied Sciences ◽

10.3390/app11114948 ◽

2021 ◽

Vol 11 (11) ◽

pp. 4948

Author(s):

Lorenzo Canese ◽

Gian Carlo Cardarilli ◽

Luca Di Di Nunzio ◽

Rocco Fazzolari ◽

Daniele Giardino ◽

...

Keyword(s):

Reinforcement Learning ◽

Mathematical Models ◽

Learning Algorithms ◽

Single Agent ◽

Critical Issues ◽

Multi Agent ◽

Pros And Cons ◽

Application Fields

In this review, we present an analysis of the most used multi-agent reinforcement learning algorithms. Starting with the single-agent reinforcement learning algorithms, we focus on the most critical issues that must be taken into account in their extension to multi-agent scenarios. The analyzed algorithms were grouped according to their features. We present a detailed taxonomy of the main multi-agent approaches proposed in the literature, focusing on their related mathematical models. For each algorithm, we describe the possible application fields, while pointing out its pros and cons. The described multi-agent algorithms are compared in terms of the most important characteristics for multi-agent reinforcement learning applications—namely, nonstationarity, scalability, and observability. We also describe the most common benchmark environments used to evaluate the performances of the considered methods.

On-Demand Channel Bonding in Heterogeneous WLANs: A Multi-Agent Deep Reinforcement Learning Approach

Sensors ◽

10.3390/s20102789 ◽

2020 ◽

Vol 20 (10) ◽

pp. 2789 ◽

Author(s):

Hang Qi ◽

Hao Huang ◽

Zhiqun Hu ◽

Xiangming Wen ◽

Zhaoming Lu

Keyword(s):

Reinforcement Learning ◽

Transmission Rate ◽

Single Agent ◽

Time Of Day ◽

Action Space ◽

Traffic Load ◽

Traffic Demand ◽

Channel Bonding ◽

On Demand ◽

Multi Agent

In order to meet the ever-increasing traffic demand of Wireless Local Area Networks (WLANs), channel bonding is introduced in IEEE 802.11 standards. Although channel bonding effectively increases the transmission rate, the wider channel reduces the number of non-overlapping channels and is more susceptible to interference. Meanwhile, the traffic load differs from one access point (AP) to another and changes significantly depending on the time of day. Therefore, the primary channel and channel bonding bandwidth should be carefully selected to meet traffic demand and guarantee the performance gain. In this paper, we proposed an On-Demand Channel Bonding (O-DCB) algorithm based on Deep Reinforcement Learning (DRL) for heterogeneous WLANs to reduce transmission delay, where the APs have different channel bonding capabilities. In this problem, the state space is continuous and the action space is discrete. However, the size of action space increases exponentially with the number of APs by using single-agent DRL, which severely affects the learning rate. To accelerate learning, Multi-Agent Deep Deterministic Policy Gradient (MADDPG) is used to train O-DCB. Real traffic traces collected from a campus WLAN are used to train and test O-DCB. Simulation results reveal that the proposed algorithm has good convergence and lower delay than other algorithms.

RELEVANCE LOGIC AND THE CALCULUS OF RELATIONS

The Review of Symbolic Logic ◽

10.1017/s1755020309990293 ◽

2010 ◽

Vol 3 (1) ◽

pp. 41-70 ◽

Cited By ~ 6

Author(s):

ROGER D. MADDUX

Keyword(s):

Propositional Logic ◽

Relevance Logic ◽

Binary Relations ◽

Classical Propositional Logic

Sound and complete semantics for classical propositional logic can be obtained by interpreting sentences as sets. Replacing sets with commuting dense binary relations produces an interpretation that turns out to be sound but not complete for R. Adding transitivity yields sound and complete semantics for RM, because all normal Sugihara matrices are representable as algebras of binary relations.