In Meyer’s promising account [7] deontic logic is reduced to a dynamic logic. Meyer claims that with his account “we get rid of most (if not all) of the nasty paradoxes that have plagued traditional deontic logic.” But as was shown by van der Meyden in [4], Meyer’s logic also contains a paradoxical formula. In this paper we will show that another paradox can be proven, one which also effects Meyer’s “solution” to contrary (...) to duty obligations and his logic in general. (shrink)

This paper suggests that it should be possible to develop dynamic deontic logic as a counterpart to the very successful development of dynamic doxastic logic (or dynamic epistemic logic, as it is more often called). The ambition, arrived at towards the end of the paper, is to give formal representations of agentive concepts such as “the agent is about to do (has just done) α ” as well as of deontic concepts such (...) as “it is obligatory (permissible, forbidden) for the agent to do α ”, where α stands for an action (event). (shrink)

In the present paper we model the Navya-Nyāya analysis of Vedic and secular injunctions and prohibitions by means of Giordani’s and Canavotto’s system ADL of dynamic deontic logic. Navya-Naiyāyikas analyze the meaning of injunctions and prohibitions by reducing them to plain indicative statements about certain properties whose presence or absence in the enjoined or prohibited action serves as a criterion for the truth or falsity of the “inducing” or “restraining knowledge”, a kind of qualificative cognition instilled in (...) the recipient of an injunction or prohibition. Thus, Navya-Naiyāyikas have found their own way to solve Jørgensen’s Puzzle concerning the very idea of a deontic logic as a tool to analyze arguments based on sentences which do not seem to be truth-apt. The teleological aspect of the Navya-Nyāya characterization of an enjoined or prohibited action can also give a clue to solutions of other puzzles and paradoxes which have beset the development of deontic logic in the West. A specific contrary-to-duty puzzle from the Indian tradition is related to the śyena, a malefic sacrifice meant for harming one’s enemy. The Vedic injunction to perform such a sacrifice runs counter to a religious practitioner’s duty not to harm a living being. In the present paper we examine the cogency of the very different solutions to this dilemma suggested by the Mīmāṃsaka Prabhākara on the one hand and the Navya-Naiyāyika Gaṅgeśa on the other hand. (shrink)

The aim of this paper is to introduce a system of dynamic deontic logic in which the main problems related to the de finition of deontic concepts, especially those emerging from a standard analysis of permission in terms of possibility of doing an action without incurring in a violation of the law, are solved. The basic idea is to introduce two crucial distinctions allowing us to differentiate (i) what is ideal with respect to a given code, (...) which fixes the types of action that are abstractly prescribed, and what is ideal with respect to the specific situation in which the agent acts, and (ii) the transitions associated with actions and the results of actions, which can obtain even without the action being performed. (shrink)

Deontic logic is standardly conceived as the logic of true statements about the existence of obligations and permissions. In his last writings on the subject, G. H. von Wright criticized this view of deontic logic, stressing the rationality of norm imposition as the proper foundation of deontic logic. The present paper is an attempt to advance such an account of deontic logic using the formal apparatus of update semantics and dynamic (...) logic. That is, we first define norm systems and a semantics of norm performatives as transformations of the norm system. Then a static modal logic for norm propositions is defined on that basis. In the course of this exposition we stress the performative nature of (i) free choice permission, (ii) the sealing legal principle and (iii) the social nature of permission. That is, (i) granting a disjunctive permission means granting permission for both disjuncts; (ii) non-prohibition does not entail permission, but the authority can declare that whatever he does not forbid is thereby permitted; and (iii) granting permission to one person means that all others are committed to not prevent the invocation of that permission. (shrink)

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. (shrink)

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. (shrink)

We present the inconsistency-adaptive deontic logic DP r , a nonmonotonic logic for dealing with conflicts between normative statements. On the one hand, this logic does not lead to explosion in view of normative conflicts such as O A ∧ O ∼A, O A ∧ P ∼A or even O A ∧ ∼O A. On the other hand, DP r still verifies all intuitively reliable inferences valid in Standard Deontic Logic (SDL). DP r interprets (...) a given premise set ‘as normally as possible’ with respect to SDL. Whereas some SDL-rules are verified unconditionally by DP r , others are verified conditionally. The latter are applicable unless they rely on formulas that turn out to behave inconsistently in view of the premises. This dynamic process is mirrored by the proof theory of DP r. (shrink)

Traditional approaches in deontic logic have focused on the so-called reportative reading of obligation sentences, by providing truth-functional semantics based on a primitive ideality order between possible worlds. Those approaches, however, do not take into account that, in natural language, obligation sentences primarily carry a prescriptive effect. The paper focuses precisely on that prescriptive character, and shows that the reportative reading can be derived from the prescriptive one. A dynamic, non truth-functional semantics for necessity deontic modals (...) is developed, in which the ideality relations among possible worlds can be updated. Finally, it is proven that the semantics solves several of the classic deontic paradoxes. (shrink)

Philosophers like G.H. von Wright and D. Makinson have pointed to serious challenges regarding the foundations of deontic logic. In this paper, I suggest that to deal successfully with these challenges a reconsideration of the research program of the discipline is useful. Some problems that have troubled this particular field of logical study for decades may disappear or appear more tractable if we view them from the perspective of a language game introduced by D. Lewis involving three characters: (...) the Master, the Slave and the Kibitzer. The adoption of this perspective opens a natural approach to a new layout of the domain of deontic studies. I propose dividing deontic logic into six sub-areas which are distinguished by their focus on the different idioms typical of the individual players, by conceiving the language game as either being static or as dynamic and by the aims of the logical inquiry. What kind of insights the proposed perspective provides is illustrated by an analysis of the so-called Ross paradox—a problem that has troubled deontic logic since its origins and, though it was many times pronounced solved, still keeps coming back ‘alive and kicking’. (shrink)

In this paper, illocutionary acts of commanding will be differentiated from perlocutionary acts that affect preferences of addressees in a new dynamic logic which combines the preference upgrade introduced in DEUL (dynamic epistemic upgrade logic) by van Benthem and Liu with the deontic update introduced in ECL II (eliminative command logic II) by Yamada. The resulting logic will incorporate J. L. Austin’s distinction between illocutionary acts as acts having mere conventional effects and perlocutionary (...) acts as acts having real effects upon attitudes and actions of agents, and help us understand why saying so can make it so in explicit performative utterances. We will also discuss how acts of commanding give rise to so-called “deontic dilemmas” and how we can accommodate most deontic dilemmas without triggering so-called “deontic explosion”. (shrink)

Although it seems intuitively clear that acts of requesting are different from acts of commanding, it is not very easy to sate their differences precisely in dynamic terms. In this paper we show that it becomes possible to characterize, at least partially, the effects of acts of requesting and compare them with the effects of acts of commanding by combining dynamified deontic logic with epistemic logic. One interesting result is the following: each act of requesting is (...) appropriately differentiated from an act of commanding with the same content, but for each act of requesting, there is another act of commanding with much more complex content which updates models in exactly the same way as it does. We will also consider an application of our characterization of acts of requesting to acts of asking yes-no questions. It yields a straightforward formalization of the view of acts of asking questions as requests for information. (shrink)

There are several formal systems for persuasive dialogue. Dialogue systems are multi-Agent systems, and this contrasts with the general lack of any agency in standard logics other than in the case of epistemic and deontic logics. Dialogue systems have been called logics. A logic usually has a semantics and a proof system, and questions of soundness and completeness arise. Any dialogue conducted according to the rules of a dialogue logic is a complex process. Dynamic Logic (...) is a logic of processes, with a possible world semantics. This paper is a preliminary exploration of transforming the dialogues of dialogue logic into complex Dynamic Logic processes with emphasis on semantic models. The transformation gives rise to many questions, three of which are discussed. Dialogue logic includes commitment sets which behave in a way similar to belief sets and undergo changes during any dialogue. There are issues as to the relationship between belief and commitment, and whether the logics of belief change apply to commitment stores. There is also the issue of the logical nature of the evaluation of dialogues as legal or illegal. (shrink)

This essay advances and develops a dynamic conception of inference rules and uses it to reexamine a long-standing problem about logical inference raised by Lewis Carroll’s regress.

We propose a new formalization of legal competences, and in particular for the Hohfeldian categories of power and immunity, through a deontic reinterpretation of dynamic epistemic logic. We argue that this logic explicitly captures the norm-changing character of legal competences while providing a sophisticated reduction of the latter to static normative positions. The logic is completely axiomatizable, and we apply it to a concrete case in German contract law to illustrate that it can capture the (...) distinction between legal ability and legal permissibility. (shrink)

The theory of imperatives is philosophically relevant since in building it — some of the long standing problems need to be addressed, and presumably some new ones are waiting to be discovered. The relevance of the theory of imperatives for philosophical research is remarkable, but usually recognized only within the field of practical philosophy. Nevertheless, the emphasis can be put on problems of theoretical philosophy. Proper understanding of imperatives is likely to raise doubts about some of our deeply entrenched and (...) tacit presumptions. In philosophy of language it is the presumption that declaratives provide the paradigm for sentence form; in philosophy of science it is the belief that theory construction is independent from the language practice, in logic it is the conviction that logical meaning relations are constituted out of logical terminology, in ontology it is the view that language use is free from ontological commitments. The list is not exhaustive; it includes only those presumptions that this paper concerns. (shrink)

Within the scope of interest of deontic logic, systems in which names of actions are arguments of deontic operators (deontic action logic) have attracted less interest than purely propositional systems. However, in our opinion, they are even more interesting from both theoretical and practical point of view. The fundament for contemporary research was established by K. Segerberg, who introduced his systems of basic deontic logic of urn model actions in early 1980s. Nowadays such (...) logics are considered mainly within propositional dynamic logic (PDL). Two approaches can be distinguished: in one of them deontic operators are introduced using dynamic operators and the notion of violation, in the other at least some of them are taken as primitive. The second approach may be further divided into the systems based on Boolean algebra of actions and the systems built on the top of standard PDL. In the present paper we are interested in the systems of deontic action logic based on Boolean algebra. We present axiomatizations of six systems and set theoretical models for them. We also show the relations among them and the position of some existing theories on the resulting picture. Such a presentation allows the reader to see the spectrum of possibilities of formalization of the subject. (shrink)

If the notion of speech acts is to be taken seriously, it must be possible to treat speech acts as acts. The development of systems of DEL (dynamic epistemic logic) in the last two decades suggests an interesting possibility. These systems are developed on the basis of static epistemic logics by introducing model updating operations to interpret various kinds of speech acts including public announcements as well as private information transmissions as what update epistemic states of agents involved. (...) The methods used in developing DEL can be used to develop logics that deal with a much wider variety of speech acts. For example, in ECL (Eliminative Command Logic) of Yamada (2007a) and ECL II of Yamada (2007b), similar model updating operations are introduced tointerpret acts of commanding as what update deontic aspects of the situations in which agents are involved. In Yamada (2008a), ECL II is further extended so as to model acts of promising along with acts of commanding. Moreover, in Yamada (2008b), ECL II is combined with a modified version of DEUL (dynamic epistemic upgrade logic) introduced in van Benthem & Liu (2007). In the resulting logic DDPL (dynamic deontic preference logic), illocutionary acts of commanding are differentiated from preference upgrading perlocutionary acts. The development of these logics suggests a recipe for developing logics that deal with various specific speech acts: first, carefully identify the aspects affected by the speech acts you want to study; second, find the modal logic that characterizes the aspects in question; and finally, add dynamic modalities that stand for the types of the speech acts being studied and define model updating operation that interprets these speech acts as what update the very aspects. (shrink)

In this paper, we analyze the relationship between commitment and obligation from a logical viewpoint. The principle of commitment implying obligation is proven in a specific logic of action preference which is a generalization of Meyer 's dynamic deontic logic. In the proposed formalism, an agent's commitment to goals is considered as a special kind of action which can change one's deontic preference andone's obligation to take some action is based on the preference and the (...) effects of the action. In this logic, it is shown that an agent has the obligation to take any action which is necessary for achieving as many committed goals as possible. The semantics of our logic is based on the possible world models for the dynamic logic of actions. A binary preference relation between possible worlds is associated with the model. Then the preference between actions are determined by comparing that of their consequences. According to the semantics, while the preference will influence the agent's choice of action, commitment is a kind of action that will change the agent's preference. Thus we can show how obligations arise from commitments via updating of deontic preference. The integrated semantics make it possible to express and reason about the mutual relationship among these mental attitudes in a common logic. (shrink)

Over the last fifteen years, linguists and philosophers of language have reexamined the canonical, Kratzerian semantics for modal expressions, with special attention paid to their epistemic and deontic uses. This article is an overview of the literature on deontic modal expressions. Section 1 provides an overview of the canonical semantics, noting some of its main advantages. Section 2 introduces a set of desiderata that have achieved the status of fixed points in the debates about whether the canonical semantics (...) is correct. These include the observations that deontic modal sentences have both deliberative and evaluative readings and both information-sensitive and -insensitive readings. Adequate resolutions of certain puzzles in deontic logic and resolving the Frege-Geach problem for Expressivism have also achieved this status. The third section provides an opinionated overview of some of the main extant rivals to the canonical semantics, including Cariani, Kaufmann, and Kaufmann’s (2013) complex contextualism , Yalcin’s (2012) Expressivism, Willer’s (2014) dynamic semantics, and Starr’s (2016) dynamic Expressivism. Section 4 provides an assessment of each of the views discussed in terms of the desiderata introduced in section 2. Section 5 is an overview of remaining issues that require more attention in the literature. (shrink)

Imperatives are linguistic devices used by an authority (speaker) to express wishes, requests, commands, orders, instructions, and suggestions to a subject (addressee). This essay's goal is to tentatively address some of the following questions about the imperative. -/- METASEMANTIC. What is the menu of options for understanding fundamental semantic notions like satisfaction, truth-conditions, validity, and entailment in the context of imperatives? Are there good imperative arguments, and, if so, how are they to be characterized? What are the options for understanding (...) the property that an account of good imperative arguments is supposed to track? What constraints on a semantic analysis of the imperative do different positions on the metasemantic issues impose? -/- SEMANTIC. How might we implement metasemantic postures in a rigorous formal system? How much can we do using familiar tools from deontic modal logic? How much leverage over semantic questions can we gain by introducing tools from natural language semantics—ordering sources, dyadic modal operators, salient alternatives, and the like—into a formal semantics for an imperative object language? How much leverage can we gain by introducing tools from rather less-utilized areas of modal logic—devices for representing actions and planning in time, modal operators constructed from action-terms, and the like—into the analysis? -/- DYNAMIC. How do imperatives succeed in performing the speech acts they are used to perform? How do imperatives update discourses? How can we leverage an account of imperative discourse update in giving a dynamic semantics for the imperative? Is there anything about the imperative that demands a dynamic semantic treatment? (shrink)

The paper investigates the way norms relate to and affect agents' intentions and actions. Current work in deontic logic dealing with agency mainly falls within two different groups: a variety of frameworks which adopt a purely external approach and represent agency in terms of possible outcomes of actions, and frameworks which instead endorse an internal approach and focus exclusively on the agents' intentions. The paper argues that neither of these models alone can produce a satisfactory analysis. An integrated (...) model which combines the internal and external approaches is therefore put forward. The model is dynamic and represents the change that accepting a goal norm triggers in an agent's intentions (especially the so-called "prior-intentions" and actions. (shrink)

Aim of the present paper is to provide a formal characterization of various different notions of responsibility within groups of agents (Who did that? Who gets the blame? Who is accountable for that? etc.). To pursue this aim, the papers proposes an organic analysis of organized collective agency by tackling the issues of organizational structure, role enactment, organizational activities, task-division and task-allocation. The result consists in a semantic framework based on dynamic logic in which all these concepts can (...) be represented and in which various notions of responsibility find a formalization. The background motivation of the work consists in those responsibility-related issues which are of particular interest for the theory and development of multi-agent systems. (shrink)

In order to deal with the possibility of deontic conflicts Lou Goble developed a group of logics (DPM) that are characterized by a restriction of the inheritance principle. While they approximate the deductive power of standard deontic logic, they do so only if the user adds certain statements to the premises. By adaptively strengthening the DPM logics, this paper presents logics that overcome this shortcoming. Furthermore, they are capable of modeling the dynamic and defeasible aspect of (...) our normative reasoning by their dynamic proof theory. This way they enable us to have a better insight in the relations between obligations and thus to localize deontic conflicts. (shrink)

An extraordinary amount of recent work by philosophers of language, meta-ethicists, and semanticists has focused on the meaning and function of language expressing concepts having to do with what is allowed, forbidden, required, or obligatory, in view of the requirements of morality, the law, one's preferences or goals, or what an authority has commanded: in short, deontic modality. This volume presents new work on the much-discussed topic of deontic modality by leading figures in the philosophy of language, meta-ethics, (...) and linguistic semantics. The papers tackle issues about the place of decision and probability theory in the semantics of deontic modality, the viability of standard possible worlds treatments of the truth conditions of deontic modal sentences, the possibility of dynamic semantic treatments of deontic modality, the methodology of semantics for deontic modals, and the prospects for representationalist, expressivist, and inferentialist treatments of deontic modality. (shrink)

We introduce a multimodal framework of deontic action logic which encodes the interaction between two fundamental procedures in normative reasoning: conceptual classification and deontic classification. The expressive power of the framework is noteworthy, since it combines insights from agency logic and dynamic logic, allowing for a representation of many kinds of normative conflicts. We provide a semantic characterization for three axiomatic systems of increasing strength, showing how our approach can be modularly extended in order (...) to get different levels of analysis of normative reasoning. Finally, we discuss ways in which the framework can be used to capture other formalisms proposed in the literature, as well as to model searching problems in Artificial Intelligence. (shrink)

Conflicts between legal norms are common in reality. In many legislations, legal conflicts between norms are resolved by applying ordered principles. This work presents a formalization of the conflict resolution mechanism and introduces action legal logic (⁠ALL) to reason about the normative consequences of possibly conflicting legal systems. The semantics of ALL is explicitly based on legal systems consisting of norms and ordered principles. Legal systems specify the legal status of transitions in transition systems and the language of ALL (...) describes the legal status of paths in transition systems. The formalization is used to study abstract revisions of legal systems. The expressivity of ALL is studied and its completeness is proved. (shrink)

This paper develops a deontic logic based on dynamic logic for reasoning about permission and prohibition of sequential actions. Our approach is characterized by two main features. First, permission and prohibition of sequential actions are not necessarily reduced to permission and prohibition of the actions’ constituent parts. Second, we incorporate the idea that actions may be permitted or prohibited conditional on another action being performed first. The logic interprets actions in terms of sequences of states, (...) and the deontic component of the logic is introduced by relating sequences of states to their legal and illegal future continuations. We consider various different logics obtained by imposing natural constraints on models, and formulate complete axiom systems for several of these logics. (shrink)

The present dissertation investigates certain facets of the logical structure of oughts – where “ought” is used as a noun, roughly meaning obligation. I do so by following two lines of inquiry. The first part of the thesis places oughts in the context of practical rationality. The second part of the thesis concerns the inference rules governing arguments about oughts, and specifically the inference rule of Reasoning by Cases. These two lines of inquiry, together, aim to expound upon oughts in (...) rationality and reasoning. The methodology used in this dissertation is the one of philosophical logic, in which logical, qualitative models are developed to support and foster conceptual analysis. The dissertation consists of four main chapters. The first two chapters are devoted to the role of oughts in practical rationality. I focus on the so-called Enkratic principle of rationality, which – in its most general formulation – requires that if an agent believes sincerely and with conviction that she ought to do X, then she intends to X. I develop a logical framework to investigate the (static and dynamic) relation between those oughts believed by the agent and her intentions. It is shown that, under certain minimal assumptions, the Enkratic principle of rationality is a principle of limited validity. The following two chapters of the dissertation constitute a study of the classical inference rule of Reasoning by Cases, which – in its simplest form – moves from the premises “A or B”, “if A then C” and “if B then C” to the conclusion “C”. Recent literature has called the validity of Reasoning by Cases into question, with the most influential counterexample being the so-called Miners’ Puzzle – an instance of Reasoning by Cases where “C” involves oughts. I provide a unifying explanation of why the Miners’ Puzzle emerges. It is shown that, within specific boundaries, Reasoning by Cases is a valid inference rule. (shrink)

Two parallelism hypotheses have been adopted and the third one on their relationship has been put forward. The illocutionary logic hypothesis states that the logic of linguistic commitments runs parallel to the logic of intentionality. The normative pragmatics hypothesis states that the logic of utterances runs parallel to the logic of linguistic commitments. According to the third stance or the logic projection hypothesis, the logic of utterances is the origin of all other logics (...) used in describing psychological and social realities. Consequently, the imperative logic or logic of utterances constitutes an independent but not self-sufficient research topic. The logic of utterances manifests itself in its meaning effects such as deontic and bouletic ones. It can be studied only in relation to deontic logics of the hearer’s obligation and the speaker’s linguistic commitments and in relation to logics of intentionality of the speaker’s expression and the hearer’s impression. Therefore, research in logic of imperative and other utterances must include investigation of relations between logics. (shrink)

Obligations can be affected by knowledge. Several approaches exist to formalize knowledge-based obligations, but no formalism has been developed yet to capture the dynamic interaction between knowledge and obligations. We introduce the dynamic extension of an existing logic for knowledge-based obligations here. We motivate the logic by analyzing several scenarios and by showing how it can capture in an original manner several fundamental deontic notions such as absolute, prima facie and all-things-considered obligations. Finally, in the (...) dynamic epistemic logic tradition, we provide reduction axioms for the dynamic operator of the new logic. (shrink)

The received wisdom on ability modals is that they differ from their epistemic and deontic cousins in what inferences they license and better receive a universal or conditional analysis instead of an existential one. The goal of this paper is to sharpen the empirical picture about the semantics of ability modals, and to propose an analysis that explains what makes the can of ability so special but that also preserves the crucial idea that all uses of can share a (...) common lexical semantics. The resulting framework combines tools and techniques from dynamic and inquisitive semantics with insights from the literature of the role of agency in deontic logic. It explains not only why the can of ability, while essentially being an existential modal operator, sometimes resists distribution over disjunction and interacts with its duals in particular and hitherto unnoticed ways, but also has a tendency to license free choice inferences. (shrink)

This paper focuses on the Enkratic principle of rationality, according to which rationality requires that if an agent sincerely and with conviction believes she ought to X, then X-ing is a goal in her plan. We analyze the logical structure of Enkrasia and its implications for deontic logic. To do so, we elaborate on the distinction between basic and derived oughts, and provide a multi-modal neighborhood logic with three characteristic operators: a non-normal operator for basic oughts, a (...) non-normal operator for goals in plans, and a normal operator for derived oughts. We prove two completeness theorems for the resulting logic, and provide a dynamic extension of the logic by means of product updates. We illustrate how this setting informs deontic logic by considering issues related to the filtering of inconsistent oughts, the restricted validity of deontic closure, and the stability of oughts and goals under dynamics. (shrink)

The programmatic statement put forward in von Wright's last works on deontic logic introduces the perspective of logical pragmatics, which has been formally explicated here and extended so to include the role of norm-recipient as well as the role of norm-giver. Using the translation function from the language of deontic logic to the language of set-theoretical approach, the connection has been established between the deontic postulates, on one side, and the perfection properties of the norm-set (...) and the counter-set, on the other side. In the study of conditions of rational norm-related activities it has been shown that diverse dynamic second-order norms related to the concept of the consistency norm-system hold: -- the norm-giver ought to restore ``classical'' consistency by revising an inconsistent system, -- the norm-recipient ought to preserve an inconsistent system by revision of its logic so that inconsistency does not imply destruction of the system. Dialetheic deontic logic of Priest is a suitable logic for the purpose since it preserves other perfection properties of the system. (shrink)

This eighteenth volume of the acclaimed Handbook of Philosophical Logic includes many contributors who are among the most famous leading figures of applied philosophical logic of our time. Coverage includes deontic logic, practical reasoning, homogeneous and heterogeneous logical proportion, and talmudic logic. Overall, it will appeal to students, practitioners, and researchers looking for an authoritative resource in these areas. The contributors first explore models in terms of dynamic logics for information-driven agency. The paradigm they (...) use is dynamic-epistemic logics for knowledge and belief and their current extensions to the statics and dynamics of agents’ preferences. Next, in the presentation of preference based agency, coverage examines a large number of themes, including interactive social agents and scenarios with long term patterns emerging over time. From here, the book moves on to offer an introduction to homogeneous and heterogeneous logical proportions. Readers will also learn more about the general challenge that the problem of formalizing practical reasoning presents to logical theory. The contributors survey the existing resources that might contribute to the development of such a formalization. They conclude that, while a robust, adequate logic of practical reasoning is not yet in place, the materials for developing such a logic are now available. The last chapter explores topics that deal with the logic of Jewish law and the logic of the Talmud. This includes obligations and prohibitions in Talmudic deontic logic, the handling of loops in Talmudic logic, Temporal Talmudic logic, and quantum states and disjunctive attacks in Talmudic logic. The Talmudic logic system presented are also exported to general logic and to Artificial Intelligence. (shrink)

We present two defeasible logics of norm-propositions (statements about norms) that (i) consistently allow for the possibility of normative gaps and normative conflicts, and (ii) map each premise set to a sufficiently rich consequence set. In order to meet (i), we define the logic LNP, a conflict- and gap-tolerant logic of norm-propositions capable of formalizing both normative conflicts and normative gaps within the object language. Next, we strengthen LNP within the adaptive logic framework for non-monotonic reasoning in (...) order to meet (ii). This results in the adaptive logics LNPr and LNPm, which interpret a given set of premises in such a way that normative conflicts and normative gaps are avoided ‘whenever possible’. LNPr and LNPm are equipped with a preferential semantics and a dynamic proof theory. (shrink)

This paper discusses the relation between deontic logic and the study of conversational interactions. Special attention is given to the notion of remedial interchange as analysed by sociologists and linguistic pragmaticians. This notion is close to the one of contrary-to-duty (reparational) obligation, which deontic logicians have been studying in its own right. The present article also investigates the question of whether some of the aspects of conversational interactions can fruitfully be described by using formal tools originally developed (...) in the study of iterated belief change. I here adapt the latter tools to deontic logic, and attempt an account of remedial interchange (and, more generally, contrary-to-duty reasoning) in terms of commutation. This account brings the dynamics of obligations to the fore. (shrink)

The aim of the paper is to introduce the concept of adaptive logics (AL) or rather adaptive logical approach. In the introduction, a motivation and an emergence of AL are briefly discussed. In the second part of the paper, specifics of AL are analysed – especially nonmonotonic character, internal and external dynamics, as well as the structure of AL, namely the distinction between upper limit logic and lower limit logic. In this part, the dynamic proof is also (...) described. Applications of AL are presented in the third part. Three illustrations from three different branches of philosophy are presented. First one is an illustration of description of science – a traditional application of AL. Second one is an illustration of solving a deontic conflict – this is a new direction within in AL which has recently been researched. Third one is an illustration of analyses of metaphors – an example of an unusual application of AL. In the conclusion of the paper, contemporary results of AL are critically evaluated with respect to some problems of the project of AL. (shrink)

A number of significant contributions in the last four decades show that non-normal modal logics can be fruitfully employed in several applied fields. Well-known domains are epistemic logic, deontic logic, and systems capturing different aspects of action and agency such as the modal logic of agency, concurrent propositional dynamic logic, game logic, and coalition logic. Semantics for such logics are traditionally based on neighbourhood models. However, other model-theoretic semantics can be used for (...) this purpose. Here, we systematically study multi-relational structures, whose investigation is still relatively underdeveloped. After a brief introduction to two different versions of multi-relational semantics – which we call strong and weak multi-relational semantics – we proceed to study several modal schemata. Special attention is paid to the schemata CON and D. Finally we offer completeness proofs for several systems using both strong and weak semantic tools: The proofs thus cover both classical system.. (shrink)

Dynamic Epistemic Logic is the logic of knowledge change. This book provides various logics to support such formal specifications, including proof systems. Concrete examples and epistemic puzzles enliven the exposition. The book also offers exercises with answers. It is suitable for graduate courses in logic. Many examples, exercises, and thorough completeness proofs and expressivity results are included. A companion web page offers slides for lecturers and exams for further practice.

Dynamic epistemic logics provide an account of the evolution of agents’ belief and knowledge when they learn the occurrence of an event. These logics started to become popular about 20 years ago and by now there exists a huge number of publications about them. The present paper briefly summarises the existing body of literature, discusses some problems and shortcomings, and proposes some avenues for future research.

This paper is devoted to the formulation and investigation of a dynamic semantic interpretation of the language of first-order predicate logic. The resulting system, which will be referred to as ‘dynamic predicate logic’, is intended as a first step towards a compositional, non-representational theory of discourse semantics. In the last decade, various theories of discourse semantics have emerged within the paradigm of model-theoretic semantics. A common feature of these theories is a tendency to do away with (...) the principle of compositionality, a principle which, implicitly or explicitly, has dominated semantics since the days of Frege. Therefore the question naturally arises whether non-compositionality is in any way a necessary feature of discourse semantics. Since we subscribe to the interpretation of compositionality as constituting primarily a methodological principle, we consider this to be a methodological rather than an empirical question. As a consequence, the emphasis in the present paper lies on developing an alternative compositional semantics of discourse, which is empirically equivalent to its non-compositional brethren, but which differs from them in a principled methodological way. Hence, no attempts are made to improve on existing theories empirically. Nevertheless, as we indicate in section 5, the development of a compositional alternative may in the end have empirical consequences, too. First of all, it can be argued that the dynamic view on interpretation developed in this paper suggests natural and relatively easy to formulate extensions which enable one to deal with a wider range of phenomena than can be dealt with in existing theories. Moreover, the various approaches to the model-theoretic semantics of discourse that have been developed during the last decade, have constituted a ‘fresh start’ in the sense that much of what had been accomplished before was ignored, at least for a start. Of course, this is a justified strategy if one feels one is trying to develop a radically different approach to recalcitrant problems. However, there comes a time when such new approaches have to be compared with the older one, and when an assessment of the pros and cons of each has to be made. One of the main problems in semantics today, we feel, is that a semantic theory such as Montague grammar, and an approach like Kamp’s discourse representation theory, are hard to compare, let alone that it is possible to unify their insights and results.. (shrink)

Epistemic logics based on the possible worlds semantics suffer from the problem of logical omniscience, whereby agents are described as knowing all logical consequences of what they know, including all tautologies. This problem is doubly challenging: on the one hand, agents should be treated as logically non-omniscient, and on the other hand, as moderately logically competent. Many responses to logical omniscience fail to meet this double challenge because the concepts of knowledge and reasoning are not properly separated. In this paper, (...) I present a dynamic logic of knowledge that models an agent’s epistemic state as it evolves over the course of reasoning. I show that the logic does not sacrifice logical competence on the altar of logical non- omniscience. (shrink)

Epistemic logic with its possible worlds semantic model is a powerful framework that allows us to represent an agent’s information not only about propositional facts, but also about her own information. Nevertheless, agents represented in this framework are logically omniscient: their information is closed under logical consequence. This property, useful in some applications, is an unrealistic idealisation in some others. Many proposals to solve this problem focus on weakening the properties of the agent’s information, but some authors have argued (...) that solutions of this kind are not completely adequate because they do not look at the heart of the matter: the actions that allow the agent to reach such omniscient state. Recent works have explored how acts of observation, inference, consideration and forgetting affect an agent’s implicit and explicit knowledge; the present work focuses on acts that affect an agent’s implicit and explicit beliefs. It starts by proposing a framework in which these two notions can be represented, and then it looks into their dynamics, first by reviewing the existing notion of belief revision, and then by introducing a rich framework for representing diverse forms of inference that involve both knowledge and beliefs. (shrink)

Dynamic Topological Logic ( ) is a modal logic which combines spatial and temporal modalities for reasoning about dynamic topological systems , which are pairs consisting of a topological space X and a continuous function f : X → X . The function f is seen as a change in one unit of time; within one can model the long-term behavior of such systems as f is iterated. One class of dynamic topological systems where the (...) long-term behavior of f is particularly interesting is that of minimal systems ; these are dynamic topological systems which admit no proper, closed, f -invariant subsystems. In such systems the orbit of every point is dense, which within translates into a non-trivial interaction between spatial and temporal modalities. This interaction, however, turns out to make the logic simpler, and while s in general tend to be undecidable, interpreted over minimal systems we obtain decidability, although not in primitive recursive time; this is the main result that we prove in this paper. We also show that interpreted over minimal systems is incomplete for interpretations on relational Kripke frames and hence does not have the finite model property; however it does have a finite non-deterministic quasimodel property. Finally, we give a set of formulas of which characterizes the class of minimal systems within the class of dynamic topological systems, although we do not offer a full axiomatization for the logic. (shrink)