arXiv subjects

Yanjing Wang

Publications and source records attributed to Yanjing Wang.

28 records · Page 2Linked to original sources

arXiv2017

A Logic of Knowing Why

When we say "I know why he was late", we know not only the fact that he was late, but also an explanation of this fact. We propose a logical framework of "knowing why" inspired by the existing formal studies on why-questions, scientific explanation, and justification logic. We introduce the Ky_i operator into the language of epistemic logic to express "agent i knows why phi" and propose a Kripke-style semantics of such expressions in terms of knowing an explanation of phi. We obtain two sound and complete axiomatizations w.r.t. two different model classes depending on different assumptions about introspection.

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arXiv2016

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 (1962). 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 (1962) 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.

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arXiv2016

Knowing Values and Public Inspection

We present a basic dynamic epistemic logic of "knowing the value". Analogous to public announcement in standard DEL, we study "public inspection", a new dynamic operator which updates the agents' knowledge about the values of constants. We provide a sound and strongly complete axiomatization for the single and multi-agent case, making use of the well-known Armstrong axioms for dependencies in databases.

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arXiv2016

"Knowing value" logic as a normal modal logic

Recent years witness a growing interest in nonstandard epistemic logics of "knowing whether", "knowing what", "knowing how", and so on. These logics are usually not normal, i.e., the standard axioms and reasoning rules for modal logic may be invalid. In this paper, we show that the conditional "knowing value" logic proposed by Wang and Fan \cite{WF13} can be viewed as a disguised normal modal logic by treating the negation of the Kv operator as a special diamond. Under this perspective, it turns out that the original first-order Kripke semantics can be greatly simplified by introducing a ternary relation $R_i^c$ in standard Kripke models, which associates one world with two $i$-accessible worlds that do not agree on the value of constant $c$. Under intuitive constraints, the modal logic based on such Kripke models is exactly the one studied by Wang and Fan (2013,2014}. Moreover, there is a very natural binary generalization of the "knowing value" diamond, which, surprisingly, does not increase the expressive power of the logic. The resulting logic with the binary diamond has a transparent normal modal system, which sharpens our understanding of the "knowing value" logic and simplifies some previously hard problems.

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arXiv2016

Achieving while maintaining: A logic of knowing how with intermediate constraints

In this paper, we propose a ternary knowing how operator to express that the agent knows how to achieve $ϕ$ given $ψ$ while maintaining $χ$ in-between. It generalizes the logic of goal-directed knowing how proposed by Yanjing Wang 2015 'A logic of knowing how'. We give a sound and complete axiomatization of this logic.

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arXiv2016

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.

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arXiv2015

From rules to runs: A dynamic epistemic take on imperfect information games

In the literature of game theory, the information sets of extensive form games have different interpretations, which may lead to confusions and paradoxical cases. We argue that the problem lies in the mix-up of two interpretations of the extensive form game structures: game rules or game runs which do not always coincide. In this paper, we try to separate and connect these two views by proposing a dynamic epistemic framework in which we can compute the runs step by step from the game rules plus the given assumptions of the players. We propose a modal logic to describe players' knowledge and its change during the plays, and provide a complete axiomatization. We also show that, under certain conditions, the mix-up of the rules and the runs is not harmful due to the structural similarity of the two.

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arXiv2015

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 phi given psi" 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.

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arXiv2013

Knowing Whether

Knowing whether a proposition is true means knowing that it is true or knowing that it is false. In this paper, we study logics with a modal operator Kw for knowing whether but without a modal operator K for knowing that. This logic is not a normal modal logic, because we do not have Kw (phi -> psi) -> (Kw phi -> Kw psi). Knowing whether logic cannot define many common frame properties, and its expressive power less than that of basic modal logic over classes of models without reflexivity. These features make axiomatizing knowing whether logics non-trivial. We axiomatize knowing whether logic over various frame classes. We also present an extension of knowing whether logic with public announcement operators and we give corresponding reduction axioms for that. We compare our work in detail to two recent similar proposals.

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arXiv2009

On expressive power and class invariance

In computer science, various logical languages are defined to analyze properties of systems. One way to pinpoint the essential differences between those logics is to compare their expressivity in terms of distinguishing power and expressive power. In this paper, we study those two concepts by regarding the latter notion as the former lifted to classes of models. We show some general results on lifting an invariance relation on models to one on classes of models, such that when the former corresponds to the distinguishing power of a logic, the latter corresponds to its expressive power, given certain compactness requirements. In particular, we introduce the notion of class bisimulation to capture the expressive power of modal logics. We demonstrate the application of our results by revisiting modal definability with our new insights.

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