Fenrong Liu

We discuss a simple logic to describe one of our favourite games from childhood, hide and seek, and show how a simple addition of an equality constant to describe the winning condition of the seeker makes our logic undecidable. There are certain decidable fragments of first-order logic which behave in a similar fashion with respect to such a language extension, and we add a new modal variant to that class. We discuss the relative expressive power of the proposed logic in comparison to the standard modal counterparts. We prove that the model checking problem for the resulting logic is \(\textsf{P}\) -complete. In addition, by exploring the connection with related product logics, we gain more insight towards having a better understanding of the subtleties of the proposed framework.

This volume contains the proceedings of DEON2020/2021, the 15th International Conference on Deontic Logic and Normative Systems that was organized by the Munich Center for Mathematical Philosophy at LMU Munich (Germany) on 21st-24th July, 2021. The biennial DEON conferences are designed to promote interdisciplinary cooperation amongst scholars interested in linking the formal-logical study of normative concepts, normative language and normative systems with computer science, artificial intelligence, linguistics, philosophy, organization theory, and law.

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.

Our preferences determine how we act and think, but exactly what the mechanics are and how they work is a central cause of concern in many disciplines. This book uses techniques from modern logics of information flow and action to develop a unified new theory of what preference is and how it changes. The theory emphasizes reasons for preference, as well as its entanglement with our beliefs. Moreover, the book provides dynamic logical systems which describe the explicit triggers driving preference change, including new information, suggestions, and commands. In sum, the book creates new bridges between many fields, from philosophy and computer science to economics, linguistics, and psychology. For the experienced scholar access to a large body of recent literature is provided and the novice gets a thorough introduction to the action and techniques of dynamic logic.

Taking the standpoint of monotonicity reasoning, this paper provides a systematic way of looking at the inference pattern mou in the Mohist text. We have taken a logical, as well as a linguistic perspective, emphasizing features of classical Chinese, the role of context, and making use of any possible clues that we can find from the old text. By applying monotonicity rules we provide a uniform account of why shi er ran examples are valid inferences, and shi er buran examples are counter-examples.

Preference is a key area where analytic philosophy meets philosophical logic. I start with two related issues: reasons for preference, and changes in preference, first mentioned in von Wright’s book The Logic of Preference but not thoroughly explored there. I show how these two issues can be handled together in one dynamic logical framework, working with structured two-level models, and I investigate the resulting dynamics of reason-based preference in some detail. Next, I study the foundational issue of entanglement between preference and beliefs, and relate the resulting richer logics to belief revision theory and decision theory.

This article proposes a systematic application of recent developments in the logic of preference to a number of topics in deontic logic. The key junction is the well‐known Hansson conditional for dyadic obligations. These conditionals are generalized by pairing them with reasoning about syntactic priority structures. The resulting two‐level approach to obligations is tested first against standard scenarios of contrary‐to‐duty obligations, leading also to a generalization for the Kanger‐Anderson reduction of deontic logic. Next, the priority framework is applied to model two intuitively different sorts of deontic dynamics of obligations, based on information changes and on genuine normative events. In this two‐level setting, we also offer novel takes on vexed issues such as the Chisholm paradox and modelling strong permission. Finally, the priority framework is shown to provide a unifying setting for the study of operations on norms as such, in particular, adding or deleting individual norms, and even merging whole norm systems in different manners.

Statements not only update our current knowledge, but also have other dynamic effects. In particular, suggestions or commands ?upgrade' our preferences by changing the current order among worlds. We present a complete logic of knowledge update plus preference upgrade that works with dynamic-epistemic-style reduction axioms. This system can model changing obligations, conflicting commands, or ?regret'. We then show how to derive reduction axioms from arbitrary definable relation changes. This style of analysis also has a product update version with preferences between actions, as well as worlds. Some illustrations are presented involving defaults and obligations. We conclude that our dynamic framework is viable, while admitting a further extension to more numerical ?utility update'

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

In this paper we explore the relationship between norms of belief revision that may be adopted by members of a community and the resulting dynamic properties of the distribution of beliefs across that community. We show that at a qualitative level many aspects of social belief change can be obtained from a very simple model, which we call ‘threshold influence’. In particular, we focus on the question of what makes the beliefs of a community stable under various dynamical situations. We also consider refinements and alternatives to the ‘threshold’ model, the most significant of which is to consider changes to plausibility judgements rather than mere beliefs. We show first that some such change is mandated by difficult problems with belief-based dynamics related to the need to decide on an order in which different beliefs are considered. Secondly, we show that the resulting plausibility-based account results in a deterministic dynamical system that is non-deterministic at the level of beliefs

The year 2012 has witnessed worldwide celebrations of Alan Turing’s 100th birthday. A great number of conferences and workshops were organized by logicians, computer scientists and researchers in AI, showing the continued flourishing of computer science, and the fruitful interfaces between logic and computer science. Logic is no longer just the concept that Frege had about one hundred years ago, let alone that of Aristotle twenty centuries before. One of the prominent features of contemporary logic is its interdisciplinary character, connecting across mathematics, philosophy, modern computer science, and even the cognitive and social sciences. China is no exception. This special issue explores interfaces of logic with AI and other disciplines, and it attempts to give a bird’s eye view of the developing landscape of logic and AI in China. Our contributors come from computer science, AI, philosophy and linguistics, united by their interest in using formal logical tools and notions to deal with substantial problems in their fields. We are aware that AI is a vast area, and that the limitations of space in a volume like this may provide a somewhat incomplete or biased view. Still we hope that the six papers selected here illustrate the concerns and curiosity driving Chinese researchers, on topics shared with our colleagues around the world. One of the active research areas in AI is planning under uncertainty, with incomplete knowledge, where a well-established logical framework is the action language of Son and Baral (Son and Baral 2001). This language can express the notions of sensing actions and making conditional plans. However, its current semantics is not yet satisfactory, since according to the semantics an agent would not have knowledge of what happens after a plan is executed, which can be a serious problem in a safety-critical environment. In their paper Proof Systems for Planning under Cautious Semantics (Shen and Zhao 2013), Yuping Shen and Xishun Zhao address this problem and propose a cautious and weakly cautious semantics for the action language. This new semantics enables the agent to know exactly what happens after executing an action. Hoare style proof systems are then proposed and proved to be sound and complete. What is more, the proposed new system reduces the reasoning complexity of the action language. In Preferential Semantics for Plausible Subsumption in Possibility Theory (Qi and Zhang 2013), Guilin Qi and Zhizheng Zhang investigate another important issue in AI: how to handle exceptions in a knowledge-based system. This has become a hot topic in recent years, especially in ontological design, where description logics are widely used. The question then arises whether we can get a nonmonotonic extension of description logic. To answer this, the authors first propose three preferential semantics for plausible subsumption in the framework of possibility theory (Dubois and Prade 1985) and study their properties and their relationships. Then they introduce preferential subsumptions to a description logic-based knowledge system, and define an entailment relation of plausible subsumption. Moreover, they study reductions of the new semantics to standard semantics for an expressive description logic. Counterfactual reasoning has been explored extensively by philosophers, cf. Lewis (1973), Stalnaker (1968). But in the last two decades, causal models have been proposed for modeling counterfactual reasoning by researchers in AI. In A Lewisian Logic of Causal Counterfactuals (Zhang 2013), Jiji Zhang studies classes of causal models and provides formal characterizations. In particular, a new logic system is proposed and proved complete for the class of ‘Lewisian models’ satisfying all the principles of David Lewis’s logic of counterfactuals. Moreover, Zhang compares his new framework with those of Lewis and Stalnaker, and also establishes formal connections with more recent approaches by Galles and Pearl, and by Halpern. Consistency is a fundamental notion in logic, but it also plays a key role in many techniques for solving constraint satisfaction problems (Mackworth 1977). In Variable-Centered Consistency in Model RB (Li et al. 2013), Liang Li, Tian Liu and Ke Xu start with a discussion of i-consistency in ‘Model RB’ and ‘Model RD’, two models of random constraint satisfaction problems with growing domain size, then compare it with the notion of t-consistency and strong t-consistency in well-known earlier work by Freuder. After that, the authors define a new kind of variable-centered consistency, and show an upper bound on a suitably chosen parameter in Model RB and Model RD, such that up to this bound, all typical instances of Model RB are variable-centered consistent. Language understanding is a cognitive process that human beings carry out every day. Metaphor is a pervasive phenomenon in natural languages, and its cognitive role calls for interpretation. There is a growing body of literature on cognitive mechanisms underlying metaphor. The paper An Ontology-Based Approach to Metaphor Cognitive Computation (Huang et al. 2013) by Xiaoxi Huang, Huaxin Huang, Beishui Liao, and Cihua Xu proposes a theoretical framework for metaphor understanding based on recent results from cognitive science (Shutova 2010). They then introduce ontology as a knowledge representation method, and present a new ontological model to formalize metaphor-based knowledge. An algorithmic description is provided using a quantitative measure of integrated degree, and its effectiveness is demonstrated. Puzzles and their solution mechanisms are a recurrent theme in many fields. Dynamic epistemic logic (van Ditmarsch et al. 2007); (van Benthem 2011) is a recent framework that can handle information dynamics in knowledge puzzles. In Reasoning About Agent Types and the Hardest Logic Puzzle Ever (Liu and Wang 2013), Fenrong Liu and Yanjing Wang propose a new dynamic-epistemic logic that can specify different types of agents and analyse agents’ knowledge, communication and reasoning. To demonstrate its power, Smullyan’s well-known Knights and Knaves puzzles are formalized, as well as the Hardest Logic Puzzle Ever (HLPE) of Boolos (Boolos 1996). Moreover, a spectrum of new puzzles is found involving knowledge-based agent types, and their solution complexity is shown to be harder than that for existing logic puzzles. It is also shown that a version of HLPE in which the agents do not know the others’ types does not have a solution at all. Finally, we would like to thank the editor of Minds and Machines, Gregory Wheeler, for his efficient assistance and kind support. We also thank Ties Nijssen at Springer for his encouragement to start this project at the first place. And of course, our appreciation goes to our authors, as well as all the colleagues who have helped us review the papers in this collection.

Diversity of agents occurs naturally in epistemic logic, and dynamic logics of information update and belief revision. In this paper we provide a systematic discussion of different sources of diversity, such as introspection ability, powers of observation, memory capacity, and revision policies, and we show how these can be encoded in dynamic epistemic logics allowing for individual variation among agents. Next, we explore the interaction of diverse agents by looking at some concrete scenarios of communication and learning, and we propose a logical methodology to deal with these as well. We conclude with some further questions on the logic of diversity and interaction.

Imperatives occur ubiquitously in natural languages. They produce forces which change the addressee’s cognitive state and regulate her actions accordingly. In real life we often receive conflicting orders, typically, issued by various authorities with different ranks. A new update semantics is proposed in this paper to formalize this idea. The general properties of this semantics, as well as its background ideas are discussed extensively. In addition, we compare our framework with other approaches of deontic logics in the context of normative conflicts.

The Asian Logic Conference (ALC) is a major international event in mathematical logic. It features the latest scientific developments in the fields of mathematical logic and its applications, logic in computer science, and philosophical logic. The ALC series also aims to promote mathematical logic in the Asia-Pacific region and to bring logicians together both from within Asia and elsewhere for an exchange of information and ideas. This combined proceedings volume represents works presented or arising from the 14th and 15th ALCs.