Logics for Knowability

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.

Linear Temporal Public Announcement Logic: a new perspective for reasoning the knowledge of multi-classifiers

Current applied intelligent systems have crucial shortcomings either in reasoning the gathered knowledge, or representation of comprehensive integrated information. To address these limitations, we develop a formal transition system which is applied to the common artificial intelligence (AI) systems, to reason about the findings. The developed model was created by combining the Public Announcement Logic (PAL) and the Linear Temporal Logic (LTL), which will be done to analyze both single-framed data and the following time-series data. To do this, first, the achieved knowledge by an AI-based system (i.e., classifiers) for an individual time-framed data, will be taken, and then, it would be modeled by a PAL. This leads to developing a unified representation of knowledge, and the smoothness in the integration of the gathered and external experiences. Therefore, the model could receive the classifier's predefined -or any external- knowledge, to assemble them in a unified manner. Alongside the PAL, all the timed knowledge changes will be modeled, using a temporal logic transition system. Later, following by the translation of natural language questions into the temporal formulas, the satisfaction leads the model to answer that question. This interpretation integrates the information of the recognized input data, rules, and knowledge. Finally, we suggest a mechanism to reduce the investigated paths for the performance improvements, which results in a partial correction for an object-detection system.

Linear Temporal Public Announcement Logic: a new perspective for reasoning the knowledge of multi-classifiers

Current applied intelligent systems have crucial shortcomings either in reasoning the gathered knowledge, or representation of comprehensive integrated information. To address these limitations, we develop a formal transition system which is applied to the common artificial intelligence (AI) systems, to reason about the findings. The developed model was created by combining the Public Announcement Logic (PAL) and the Linear Temporal Logic (LTL), which will be done to analyze both single-framed data and the following time-series data. To do this, first, the achieved knowledge by an AI-based system (i.e., classifiers) for an individual time-framed data, will be taken, and then, it would be modeled by a PAL. This leads to developing a unified representation of knowledge, and the smoothness in the integration of the gathered and external experiences. Therefore, the model could receive the classifier's predefined -or any external- knowledge, to assemble them in a unified manner. Alongside the PAL, all the timed knowledge changes will be modeled, using a temporal logic transition system. Later, following by the translation of natural language questions into the temporal formulas, the satisfaction leads the model to answer that question. This interpretation integrates the information of the recognized input data, rules, and knowledge. Finally, we suggest a mechanism to reduce the investigated paths for the performance improvements, which results in a partial correction for an object-detection system.

Labelled Natural Deduction for Public Announcement Logic with Common Knowledge

Public announcement logic is a logic that studies epistemic updates. In this paper, we propose a sound and complete labelled natural deduction system for public announcement logic with the common knowledge operator (PAC). The completeness of the proposed system is proved indirectly through a Hilbert calculus for PAC known to be complete and sound. We conclude with several discussions regarding the system including some problems of the system in attaining normalisation and subformula property.

A cut-free labelled sequent calculus for dynamic epistemic logic

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.

Model checking for coalition announcement logic

This talk is based on joint work with Rustam Galimullin and Hans van Ditmarsh, published in the German Conference on Artificial Intelligence (KI 2018). First I will introduce background and motivation for the work. I will introduce multi-agent Epistemic Logic (EL) for representing knowledge of (idealised) agents, Public Announcement Logic (PAL) for modelling knowledge change after truthful announcements, Group Announcement Logic (GAL) for modelling what kinds of changes in other agents’ knowledge a group of agents can effect, and Coalition Announcement Logic (CAL) which is the main subject of the talk. CAL studies how a group of agents can enforce a certain outcome by making a joint announcement, regardless of any announcements made simultaneously by the opponents. The logic is useful to model imperfect information games with simultaneous moves. It is also useful for devising protocols of announcements that will increase some knowledge of some agents, but also preserve other agents’ ignorance with respect to some information (in other words, preserve privacy of the announcers). The main new technical result in the talk is a model checking algorithm for CAL, that is, an algorithm for evaluating a CAL formula in a given finite model. The model-checking problem for CAL is PSPACE-complete, and the protocol requires polynomial space (but exponential time). DOI: 10.21146/2074-1472-2018-24-2-59-69

Reasoning about knowledge and messages in asynchronous multi-agent systems

We propose a variant of public announcement logic for asynchronous systems. To capture asynchrony, we introduce two different modal operators for sending and receiving messages. The natural approach to defining the semantics leads to a circular definition, but we describe two restricted cases in which we solve this problem. The first case requires the Kripke model representing the initial epistemic situation to be a finite tree, and the second one only allows announcements from the existential fragment. After establishing some validities, we study the model checking problem and the satisfiability problem in cases where the semantics is well-defined, and we provide several complexity results.