Fenrong Liu

This book presents established and new research on the close connections between graph games and systems of logic, particularly existing and newly designed modal logics. The volume utilizes two graph games – the sabotage game and the hide-and-seek game – to demonstrate the natural interplay between designing new graph games and exploring new kinds of logics that fit with these games. The collected works in this volume therefore straddle both established research directions of designing logics for analyzing games and designing games for analyzing logics. This book contains a general introduction to the project of matching up graph games and logic design, and a collection of selected and commissioned contributions that illustrate novel concepts, questions, and logical techniques in the field. The contributions are introduced and contextualized in an editorial preface and conclusion. Future outlooks towards further research on graph games, new graph games, major new technical challenges, and potential practical applications to, for example, board games and a design tool for experiments in cognitive psychology conclude the volume. This book is of interest to a broad audience working with theoretical and practical applications of graph games and modal logics.

In the tradition of memory logic, two comparatively weak systems, poison modal logic (PML) and poison sabotage logic (PSL), were studied in existing literature to capture the so-called poison game, which originally served as a paradigm to reason about graph- theoretical notions and was recently shown to have important applications in the theory of abstract argumentation. In this work, we continue to explore the technical aspect of the two logics and complete the existing results by providing our solutions to the questions identified in the literature [19, 20, 13]. Precisely, we show that (i) neither of them can be embedded in fixed-variable fragment of first-order logic, on the basis of the existing findings for PML and PSL, (ii) PSL has an undecidable satisfiability problem, and (iii) motivated by the existing axiomatization results for the standard memory logic [5], we axiomatize the two logics in a broader setting with enrichments from hybrid logic. As we shall see, in line with the fact that PSL is strictly weaker than PML, the calculus for the hybrid PSL developed will also be a ‘fragment’ of that for the hybrid PML.

The game of Cops and Robbers is an important model for studying computa-tional queries in pursuit-evasion environments, among others. As recent logical explorations have shown, its structure exhibits appealing analogies with modal logic. In this paper, we enrich the game with a setting in which players may have imperfect information. We propose a new formal framework, Epistemic Logic of Cops and Robbers (ELCR), to make the core notions of the game precise, for instance, players’ positions, observational power and inference. Applying ELCR to analyze the game, we obtain an automated way to track interactions between players and characterize their information updates during the game. The update mechanism is defined by a novel dynamic operator, and we compare it with some relevant paradigms from the game and logic perspectives. We study various prop-erties of ELCR including axiomatization and decidability. To our knowledge, this is the first attempt to explore these games from a formal point of view where (partial) information available to players is taken into account.

The concept of preference spans numerous research fields, resulting in diverse perspectives on the topic. Preference logic specifically focuses on reasoning about preferences when comparing objects, situations, actions, and more, by examining their formal properties. This entry surveys major developments in preference logic to date. Section 2 provides a historical overview, beginning with foundational work by Halldén and von Wright, who emphasized the syntactic aspects of preference. In Section 3, early semantic contributions by Rescher and Van Dalen are introduced. The consideration of preference relations over possible worlds naturally gives rise to modal preference logic where preference lifting enables comparisons across sets of possible worlds. Section 4 introduces von Wright’s distinction between intrinsic and extrinsic preferences and presents a two-layer structure for extrinsic (or reason-based) preferences, a major focus of development over the last two decades. This entry reviews the primary frameworks in this area. Section 5 is about preference change, which can happen for various reasons, and it explores different logical approaches to these dynamics. Section 6 discusses various interpretations of ceteris paribus preferences, provides a review of its underlying logic, and examines conditional preference networks (CP-nets), which are closely related to this concept. Section 7 briefly examines the connections between preference logic and other research areas. Section 8 concludes this entry.

The notion of preference is important in philosophy, decision theory, and many other disciplines. It is the interplay of information and preferences that provides the driving force behind what we actually do. The chapter adds a new focus and argues that preference is not static, instead, it changes dynamically when triggered by various kinds of events. We show that how a wide variety of preference changes can be modeled in logic, thereby providing the formal philosopher with a natural extension of the scope of inquiry in the area of preference.

The normative realm involves deontic notions such as obligation or permission, as well as information about relevant actions and states of the world. This mixture is not static, given once and for all. Both information and normative evaluation available to agents are subject to changes with various triggers, such as learning new facts or accepting new laws. This paper explores models for this setting in terms of dynamic logics for information-driven agency. Our paradigm will be dynamic-epistemic logics for knowledge and belief, and their current extensions to the statics and dynamics of agents’ preferences. Here the link with deontics is that moral reasoning may be viewed as involving preferences of the acting agent as well as preferences of moral authorities such as lawgivers, one’s conscience, or yet others. In our presentation of preference based agency, we discuss a large number of themes: primitive ‘betterness’ order versus reason-based preferences (employing a model of ‘priority graphs’), the entanglement of preference and informational attitudes such as belief, interactive social agents, and scenarios with longterm patterns emerging over time. Specific deontic issues considered include paradoxes of deontic reasoning, acts of changing obligations, and changing norm systems. We conclude with some further directions, such as multi-agency and games, plus pointers to related work, including different paradigms for looking at these same phenomena.

This article examines the usage of zhou 周 in the Book of Mozi 墨子 and its interpretations in Classical Chinese, arguing that zhou functions as a universal quantifier when placed before verb–object constructions. We contend that the concluding statement “yi zhou er yi bu zhou” 一周而一不周 clarifies the validity of the case “shi er ran” 是而然 and the invalidity of “shi er bu ran” 是而不然 by using zhou as a summary term referring to previous discussions. Our analysis of zhou as a universal quantifier and you 有 as an existential quantifier provides a foundation for employing the monotonicity reasoning approach to study mou 侔 reasoning. This insight may shed light on other reasoning patterns in Mohist logic and beyond.

History of Logic in China: 5 Questions is a collection of short interviews based on 5 questions presented to some of the most influential and prominent scholars in the field. We hear their views on the field, the aim, the scopes, the future direction of research and how their work fits in these respects. Interviews with Rens Bod, Chung-Ying Cheng, Cui Qingtian, Dong Zhitie, Chris Fraser, Yiu-Ming Fung, Jane Geaney, Chad Hansen, Christoph Harbsmeier, Ju Zhonglin, Hsien-Chung Lee, Jer-Shiarn Lee, Michiel Leezenberg, Liu Peiyu, Thierry Lucas, Gregor Paul, Dan Robins, Shen Jianying, Sun Zhongyuan, Wang Kexi, Yang Wujin, Zhai Jincheng, Zheng Weihong, Zhou Shan and Zhou Yunzhi.

Edited in collaboration with FoLLI, the Association of Logic, Language and Information this book constitutes the refereed proceedings of the Second Interdisciplinary Workshop on Logic, Language, and Meaning, TLLM 2020, held in Tsinghua, China, in December 2020. The 12 full papers together presented were fully reviewed and selected from 40 submissions. Due to COVID-19 the workshop will be held online. The workshop covers a wide range of topics where monotonicity is discussed in the context of logic, causality, belief revision, quantification, polarity, syntax, comparatives, and various semantic phenomena in particular languages.

Modern logic is an active agent all across the university today, connecting disciplines, and transcending traditional boundaries. This book demonstrates this general role in the special setting of a conference at Tsinghua University, where modern logic was already taught in the 1930s by pioneers like Jin Yeulin. This boon contains an unusual dialogue between Chinese logicians and international colleagues representing a wide range of disciplines, including philosophy, mathematics, linguistics computer science, cognitive science, and the social sciences. The focus of this encounter is not only to advance logic in its university-wide role but also to look for its application in modern society.

This three-volume set—LNAI 13031, LNAI 13032, and LNAI 13033—constitutes the thoroughly refereed proceedings of the 18th Pacific Rim Conference on Artificial Intelligence (PRICAI 2021), held in Hanoi, Vietnam, in November 2021. The 93 full papers and 28 short papers presented in these volumes were carefully reviewed and selected from 382 submissions. PRICAI covers a wide range of topics of social and economic importance for countries in the Pacific Rim, including artificial intelligence, machine learning, natural language processing, knowledge representation and reasoning, planning and scheduling, computer vision, distributed artificial intelligence, and search methodologies. Part I includes the following topical headings: AI Foundations / Decision Theory, Applications of AI, Data Mining and Knowledge Discovery, Evolutionary Computation / Optimization, and Knowledge Representation and Reasoning.

This three-volume set, LNCS 14325-14327 constitutes the thoroughly refereed proceedings of the 20th Pacific Rim Conference on Artificial Intelligence, PRICAI 2023, held in Jakarta, Indonesia, in November 2023. The 95 full papers and 36 short papers presented in these volumes were carefully reviewed and selected from 422 submissions. PRICAI covers a wide range of topics in the areas of social and economic importance for countries in the Pacific Rim: artificial intelligence, machine learning, natural language processing, knowledge representation and reasoning, planning and scheduling, computer vision, distributed artificial intelligence, search methodologies, etc.

In this paper we consider preference over objects. We show how this preference can be derived from priorities, properties of these objects, a concept which is initially from optimality theory. We do this both in the case when an agent has complete information and in the case when an agent only has beliefs about the properties. After the single agent case we also consider the multi-agent case. In each of these cases, we construct preference logics, some of them extending the standard logic of belief. This leads to interesting connections between preference and beliefs. We strengthen the usual completeness results for logics of this kind to representation theorems. The representation theorems describe the reasoning that is valid for preference relations that have been obtained from priorities. In the multi-agent case, these representation theorems are strengthened to the special cases of cooperative and competitive agents. We study preference change with regard to changes of the priority sequence, and change of beliefs. We apply the dynamic epistemic logic approach, and in consequence reduction axioms are presented. We conclude with some possible directions for future work.

It has usually been assumed that monadic value notions can be defined in terms of dyadic value notions, whereas definitions in the opposite direction are not possible. In this paper, inspired by van Benthem’s work, it is shown that the latter direction is feasible with a method in which shifts in context have a crucial role. But although dyadic preference orderings can be defined from context-indexed monadic notions, the monadic notions cannot be regained from the preference relation that they gave rise to. Two formal languages are proposed in which reasoning about context can be represented in a fairly general way. One of these is a modal language much inspired by van Benthem’s work. Throughout the paper the focus is on relationships among the value notions “good”, “bad”, and “better”. Other interpretations like “tall” and “taller” are equally natural. It is hoped that the results of this paper can be relevant for the analysis of natural language comparatives and of vague predicates in general.

In this article, we study a minimal change approach to preference dynamics. We treat a set of preferences as a special kind of theory, and define minimal change preference contraction and revision operations in the spirit of the Alchourrón, Gärdenfors, and Makinson theory of belief revision. We characterise minimal contraction of preference sets by a set of postulates and prove a representation theorem. We also give a linear time algorithm which implements minimal contraction by a single preference. We then define minimal contraction by a set of preferences, and show that the problem of a minimal contraction by a set of preferences is NP-hard.

New perspectives keep emerging in the logical study of social interactions, witnessed by yet another collection of research papers. Once our focus of reasoning shifts from an individual to a social setting, interesting issues naturally arise. The central question is the following: how is an individual’s attitude related to that of others and that of a group, especially when we take into account the informative communication between agents, as well as the structures of a group? This has been studied to various extent in social epistemology, social choice theory, social norms theory, etc. In this context, our main concern is logic: how can a logical approach shed light on our reasoning about these scenarios? We are not giving a comprehensive overview but just to mention some research that is mostly relevant. Communication between agents, public or private, has been extensively studied in dynamic epistemic logic (e.g. [1, 9, 10]) and dynamic epistemic logic has become a standard methodology in modelling dynamical changes of agent’s attitudes. Social network logics have been developed recently, adding social structures of a group as a core component to logic models and formal languages [2, 5–8, 11]. The papers included in this special issue provide us with further new insights about our understanding of social settings. In what follows, we briefly summarize their ideas and some main results.

This thesis investigates two main issues concerning the behavior of rational agents, preference dynamics and agent diversity. We take up two questions left aside by von Wright, and later also the multitude of his successors, in his seminal book Logic of Preference in 1963: reasons for preference, and changes in preference. Various notions of preference are discussed, compared and further correlated in the thesis. In particular, we concentrate on extrinsic preference. Contrary to intrinsic preference, extrinsic preference is reason-based, i.e. one's preference for one option over another has a reason. A logical model is proposed and its properties are determined. Dynamics come in naturally, since reasons for the preferences can change. Logical systems and formal results regarding dynamical preference change are then presented. Preference arises from comparisons between alternatives. A first option is to compare situations. Abstractly speaking, preferences are in this case between propositions, viewed as sets of possible worlds. The reasons can then be based on a `betterness' relation over possible worlds. Propositional preference arises as a lift from this primitive relation. A standard modal logical approach is taken and we use a modality for the betterness relation in the language. We then model preference change by techniques from dynamic epistemic logic (DEL), where a typical action, e.g. a suggestion or a command can change the betterness ordering of the worlds, and thereby the propositional preference. Dynamic reduction axioms are obtained to encode exactly how such a change takes place. We obtain a complete dynamic preference logic. A second option is to compare objects as such. Concretely, properties of the objects often determine the preference over the objects. Properties are now the reasons. Inspired by Optimality Theory (OT), we propose a priority sequence, an ordering of properties. Various ways of getting a preference from the priority sequence are investigated, though we mostly follow the OT approach. We use a fragment of first-order logic to describe the situation. Here, on the dynamic side, it is priority change that leads to preference change. Using the DEL methodology again we propose a complete set of reduction axioms concerning the possible dynamic operations on priority sequences. Not surprisingly, the above two views are closely related. After all, possible worlds can be thought of as objects! On the basis of a systematic comparison of the two views, we develop a two level perspective, in which the models themselves are structured in layers. In particular, correspondence results between the changes at the level of the possible worlds and the changes at the level of the priority sequences are proved. We end up by sketching a two-level preferential predicate logic to describe more complex circumstances in which situations and objects are compared simultaneously. But we do not see this as the whole story. Preference does not live by itself, it is often intermingled with epistemic notions of knowledge and belief. One can have different intuitions about how this entanglement operates. A few options are discussed, and proposals for logical models are presented. When moving to dynamics, we now see a picture of knowledge update, belief revision and preference change taking place symbiotically, often unconsciously as in real life. The resulting picture in the thesis is one of agents that process information and adjust beliefs and preferences in many different ways. There is no logically prescribed unique norm for doing this. The second part of the thesis takes this general phenomenon of diversity of agents as its focus, since it raises many issues for logical systems and the idealized agents which they normally presuppose. In reality, agents can differ across a wide spectrum of cognitive abilities and habits: in their memory capacity, observation power, inferential power, introspective ability, and revision policies when facing new information. Two kinds of agents, perfect recall agents, and memory-free agents are studied thoroughly, in the setting of playing games. We show how current dynamic logics can be `parametrized' to allow for this memory diversity, with new characterizations of agent types resulting in complete dynamic-epistemic logics. The other dimension of the reality of diverse agents is that, however different they are, they often do manage to coordinate with each other successfully. While this theme has been prominent in game theory and multi-agent systems, it has received hardly any attention in logic. We analyze this interaction between different agents by looking at concrete scenarios which model their types explicitly. Finally, we analyze the issue of agent diversity in its generality, discussing what dynamic logics would have to look like to become a full-fledged account of agents of different capacities and tendencies that pursue and sometimes achieve their goals in irreducibly social settings.

Graph games are interactive scenarios with a wide range of applications. This position paper discusses old and new graph games in tandem with matching logics and identifies general questions behind this match. Throughout, we pursue two strands: logic as a way of analyzing existing graph games, and logic as an inspiration for designing new graph games. Our aim is modest: we propose a perspective that complements existing game-theoretic and computational ones, we raise questions, make observations, and suggest research directions—technical results are left to future work. But frankly, our main aim with this survey paper is to show that graph games are concrete, fun, easy to grasp, and yet challenging to study.

Dynamic epistemic logic (DEL) extends purely modal epistemic logic (S5) by adding dynamic operators that change the model structure. Propositional dynamic logic (PDL) extends basic modal logic with programs that allow the de nition of complex modalities. We provide a common generalisation: a logic that is dynamic in both senses, and one that is not limited to S5 as its modal base. It also incorporates, and signi cantly generalises, all the features of existing extensions of DEL such as BMS [3] and LCC [21]. Our dynamic operators work in two steps. First, they provide a multiplicity of transformations of the original model, one for each action in a purely syntactic action structure (in the style of BMS). Second, they specify how to combine these multiple copies to produce a new model. In each step, we use the generality of PDL to specify the transformations. The main technical contribution of the paper is to provide an axiomatisation of this general dynamic dynamic logic (GDDL). This is done by providing a computable translation of GDDL formulas to equivalent PDL formulas, thus reducing the logic to PDL, which is decidable. The proof involves switching between representing programs as terms and as automata. We also show that both BMS and LCC are special cases of GDDL, and that there are interesting applications that require the additional generality of GDDL, namely the modelling of private belief update. More recent extensions and variations of BMS and LCC are also discussed.

The logic of the hide and seek game $$\textbf{LHS}$$ was proposed to capture interactions between agents in pursuit-evasion environments. In this paper, we explore a hybrid extension of $$\textbf{LHS}$$ and show that such an extension is beneficial in several aspects. We will show that it improves the technical properties of the resulting logical system, and expands the potential applications of the system. Specifically, we will investigate the expressive power of the hybrid logic of the hide and seek game $${\mathcal {H}}(\textbf{LHS})$$ and its crucial fragment $${\mathcal {H}}(\textbf{LHS}^{-})$$, at both model and frame levels. We will present complete Hilbert-style proof systems for both the logics $${\mathcal {H}}(\textbf{LHS}^{-})$$ and $${\mathcal {H}}(\textbf{LHS})$$, which in fact provides a solution to a known open problem.

This book provides a first introduction to two key systems that play a role in any variety or application of logic: classical propositional logic and classical predicate logic. It also contains pointers to variations and alternatives, to logics that deal with a wider range of concepts. This book provides examples of the application of logic to philosophical problems, and illustrates some of the philosophical problems that are raised by logic itself. This book aims to give the reader a first glimpse of the wide variety of tastes, smells, and textures that await them once they have trained their palate to appreciate the standard dishes of the logic cuisine.