Yanjing Wang

On the logic of lying

We model lying as a communicative act changing the beliefs of the agents in a multi-agent system. With Augustine, we see lying as an utterance believed to be false by the speaker and uttered with the intent to deceive the addressee. The deceit is successful if the lie is believed after the utterance by the addressee. This is our perspective. Also, as common in dynamic epistemic logics, we model the agents addressed by the lie, but we do not (necessarily) model the speaker as one of those agents. This further simplifies the picture: we do not need to model the intention of the speaker, nor do we need to distinguish between knowledge and belief of the speaker: he is the observer of the system and his beliefs are taken to be the truth by the listeners. We provide a sketch of what goes on logically when a lie is communicated. We present a complete logic of manipulative updating, to analyse the effects of lying in public discourse. Next, we turn to the study of lying in games. First, a game-theoretical analysis is used to explain how the possibility of lying makes games such as Liars Dice interesting, and how lying is put to use in optimal strategies for playing the game. This is the opposite of the logical manipulative update: instead of always believing the utterance, now, it is never believed. We also give a matching logical analysis for the games perspective, and implement that in the model checker DEMO. Our running example of lying in games is the game of Liars Dice.

Propositional Dynamic Logic as a Logic of Belief Revision

This paper shows how propositional dynamic logic (PDL) can be interpreted as a logic for multi-agent belief revision. For that we revise and extend the logic of communication and change (LCC) of [9]. Like LCC, our logic uses PDL as a base epistemic language. Unlike LCC, we start out from agent plausibilities, add their converses, and build knowledge and belief operators from these with the PDL constructs. We extend the update mechanism of LCC to an update mechanism that handles belief change as relation substitution, and we show that the update part of this logic is more expressive than either that of LCC or that of doxastic/epistemic PDL with a belief change modality. It is shown that the properties of knowledge and belief are preserved under any update, and that the logic is complete.

Contingency and knowing whether

A proposition is noncontingent, if it is necessarily true or it is necessarily false. In an epistemic context, ‘a proposition is noncontingent’ means that you know whether the proposition is true. In this paper, we study contingency logic with the noncontingency operator Δ but without the necessity operator □. This logic is not a normal modal logic, because Δ( φ → ψ ) → (Δ φ → Δ ψ ) is not valid. Contingency logic cannot define many usual frame properties, and its expressive power is weaker than that of basic modal logic over classes of models without reflexivity. These features make axiomatizing contingency logics nontrivial, especially for the axiomatization over symmetric frames. In this paper, we axiomatize contingency logics over various frame classes using a novel method other than the methods provided in the literature, based on the ‘almost-definability’ schema AD proposed in our previous work. We also present extensions of contingency logic with dynamic operators. Finally, we compare our work to the related work in the fields of contingency logic and ignorance logic, where the two research communities have similar results but are apparently unaware of each other’s work. One goal of our paper is to bridge this gap.

A Logic of Knowing How

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 know how to guarantee ϕ given ψ” with a semantics not based on standard epistemic models but labelled transition systems that represent the agent’s knowledge of his own abilities. A sound and complete proof system is given to capture the valid reasoning patterns about “knowing how” where the most important axiom suggests its compositional nature.

Reasoning About Agent Types and the Hardest Logic Puzzle Ever

In this paper, we first propose a simple formal language to specify types of agents in terms of necessary conditions for their announcements. Based on this language, types of agents are treated as ‘first-class citizens’ and studied extensively in various dynamic epistemic frameworks which are suitable for reasoning about knowledge and agent types via announcements and questions. To demonstrate our approach, we discuss various versions of Smullyan’s Knights and Knaves puzzles, including the Hardest Logic Puzzle Ever (HLPE) proposed by Boolos (in Harv Rev Philos 6:62–65, 1996). In particular, we formalize HLPE and verify a classic solution to it. Moreover, we propose a spectrum of new puzzles based on HLPE by considering subjective (knowledge-based) agent types and relaxing the implicit epistemic assumptions in the original puzzle. The new puzzles are harder than the previously proposed ones in the literature, in the sense that they require deeper epistemic reasoning. Surprisingly, we also show that a version of HLPE in which the agents do not know the others’ types does not have a solution at all. Our formalism paves the way for studying these new puzzles using automatic model checking techniques.

To know or not to know: epistemic approaches to security protocol verification

Security properties naturally combine temporal aspects of protocols with aspects of knowledge of the agents. Since BAN-logic, there have been several initiatives and attempts to incorporate epistemics into the analysis of security protocols. In this paper, we give an overview of work in the field and present it in a unified perspective, with comparisons on technical subtleties that have been employed in different approaches. Also, we study to which degree the use of epistemics is essential for the analysis of security protocols. We look for formal conditions under which knowledge modalities can bring extra expressive power to pure temporal languages. On the other hand, we discuss the cost of the epistemic operators in terms of model checking complexity.

Beyond Knowing That: A New Generation of Epistemic Logics

Epistemic logic has become a major field of philosophical logic ever since the groundbreaking work by Hintikka [58]. Despite its various successful applications in theoretical computer science, AI, and game theory, the technical development of the field has been mainly focusing on the propositional part, i.e., the propositional modal logics of “knowing that”. However, knowledge is expressed in everyday life by using various other locutions such as “knowing whether”, “knowing what”, “knowing how” and so on (knowing-wh hereafter). Such knowledge expressions are better captured in quantified epistemic logic, as was already discussed by Hintikka [58] and his sequel works at length. This paper aims to draw the attention back again to such a fascinating but largely neglected topic. We first survey what Hintikka and others did in the literature of quantified epistemic logic, and then advocate a new quantifier-free approach to study the epistemic logics of knowing-wh, which we believe can balance expressivity and complexity, and capture the essential reasoning patterns about knowing-wh. We survey our recent line of work on the epistemic logics of ‘knowing whether”, “knowing what” and “knowing how” to demonstrate the use of this new approach.

A Dynamic Epistemic Framework for Conformant Planning

In this paper, we introduce a lightweight dynamic epistemic logical framework for automated planning under initial uncertainty. We reduce plan verification and conformant planning to model checking problems of our logic. We show that the model checking problem of the iteration-free fragment is PSPACE-complete. By using two non-standard (but equivalent) semantics, we give novel model checking algorithms to the full language and the iteration-free language.

Refinement of Kripke Models for Dynamics

We propose a property-preserving refinement/abstraction theory for Kripke Modal Labelled Transition Systems incorporating not only state mapping but also label and proposition lumping, in order to have a compact but informative abstraction. We develop a 3-valued version of Public Announcement Logic (PAL) which has a dynamic operator that changes the model in the spirit of public broadcasting. We prove that the refinement relation on staticmodels assures us to safely reason about any dynamicproperties in terms of PAL-formulas on the abstraction of a model. The theory is in particular interesting and applicable for an epistemic setting as the example of the Muddy Children puzzle shows, especially in the view of the growing interest for epistemic modelling and (automatic) verification of communication protocols.

A logic of goal-directed knowing how

In this paper, we propose a decidable single-agent modal logic for reasoning about goal-directed “knowing how”, based on ideas from linguistics, philosophy, modal logic, and automated planning in AI. We first define a modal language to express “I know how to guarantee