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.

Multi-modal versions of propositional logics S5 or S4—commonly accepted as logics of knowledge—are capable of describing static states of knowledge but they do not reflect how the knowledge changes after communications among agents. In the present paper (part of broader research on logics of knowledge and communications) we define extensions of the logic S5 which can deal with public communications. The logics have natural semantics. We prove some completeness, decidability and interpretability results and formulate a general method that solves certain (...) kind of problems involving public communications—among them well known puzzles of Muddy Children and Mr. Sum & Mr. Product. As the paper gives a formal logical treatment of the operation of restriction of the universe of a Kripke model, it contributes also to investigations of semantics for modal logics. (shrink)

It is the aim of INDICES to document recent explorations in the various fields of philosophical logic and formal linguistics and their applications in other disciplines. The main emphasis of this series is on self-contained monographs covering particular areas of recent research and surveys of methods, problems, and results in all fields of inquiry where recourse to logical analysis and logical methods has been fruitful. INDICES will contain monographs dealing with the central areas of philosophical logic (extensional and intensional systems, (...) indexical logics, non-classical logics, philosophy of logic, etc.) as well as studies in which these systems are applied to specific issues in philosophy, in the formal semantics of natural languages, the foundations of linguistic theory, in computational linguistics, and in theoretical computer science. Constructive type theory was first presented in 1970, by the Swedish logician Per Martin-Lof. It has become one of the main approaches used in the foundations of mathematics and computer science. But it has remained relatively unknown among linguists and philosophers, although it provides a considerable extension of the concepts and techniques of logic. The book first gives an introduction to type theory from the point of view of linguistics and the philosophy of language. Type theory is then applied in the areas of quantification, anaphora, temporal reference, and the structure of text and discourse. By virtue of the type-theoretical concepts of proof object and context, various phenomena of dependence and progression in language can be discussed in precise terms, and several well-known problems can be solved. A categorial grammar is presented togenerate formally a fragment of English, together with an example of a computer implementation. (shrink)

The existing literature treats of several investigations with a certain bearing on the question which is roughly indicated by the title “Imperatives and Logic.” Some of those investigations, however, are entirely outside the scope of the present work.Mally sets himself the task of developing a “Logik des Willens” constituting a parallel to the usual logic, the “Logik des Denkens". In order to emphasize its independence, the author also calls this “Logik des Willens” “Deontik”, and he conceives it as being based (...) on the “Wesensgesetze” of will in the same way as the usual logic is conceived as being based on the “Wesensgesetze” of thought. The author develops a formalistic deductive system on the basis of 5 axioms of demands, including the axiom that there is at least one fact which is unconditionally demanded, and through a lengthy series of theorems he arrives at the sentence that what is unconditionally demanded is identical with what is actually the case: “was sein soll, ist Tatsache”. Similarly, the author develops a system of axioms for “right” volition, including the axiom that right volition is non-contradictory. (shrink)

This book presents an in-depth interpretation of three important parts of Leibniz's metaphysics: the metaphysical part of Leibniz's philosophy of logic, his essentially theological treatment of the central issues of ontology, and his theory of substance.

Imperatives cannot be true or false, so they are shunned by logicians. And yet imperatives can be combined by logical connectives: "kiss me and hug me" is the conjunction of "kiss me" with "hug me". This example may suggest that declarative and imperative logic are isomorphic: just as the conjunction of two declaratives is true exactly if both conjuncts are true, the conjunction of two imperatives is satisfied exactly if both conjuncts are satisfied—what more is there to say? Much more, (...) I argue. "If you love me, kiss me", a conditional imperative, mixes a declarative antecedent ("you love me") with an imperative consequent ("kiss me"); it is satisfied if you love and kiss me, violated if you love but don't kiss me, and avoided if you don't love me. So we need a logic of three -valued imperatives which mixes declaratives with imperatives. I develop such a logic. (shrink)

In a world plagued by disagreement and conflict one might expect that the exact sciences of logic and mathematics would provide a safe harbor. In fact these disciplines are rife with internal divisions between different, often incompatible, systems. Do these disagreements admit of resolution? Can such resolution be achieved without disturbing assumptions that the theorems of logic and mathematics state objective truths about the real world? In this original and historically rich book John Woods explores apparently intractable disagreements in logic (...) and the foundations of mathematics and sets out conflict resolution strategies that evade or disarm these stalemates. An important sub-theme of the book is the extent to which pluralism in logic and the philosophy of mathematics undermines realist assumptions. This book makes an important contribution to such areas of philosophy as logic, philosophy of language and argumentation theory. It will also be of interest to mathematicians and computer scientists. (shrink)

Hans Kelsen is considered by many to be the foremost legal thinker of the twentieth century. During the last decade of his life he was working on what he called a general theory of norms. Published posthumously in 1979 as Allgemeine Theorie der Normen, the book is here translated for the first time into English. Kelsen develops his "pure theory of law" into a "general theory of norms", and analyzes the applicability of logic to norms to offer an original and (...) extreme position which some have called "normative irrationalism". Examining the views of over 200 philosophers and legal theorists on law, morality, and logic, and revising several of his own earlier positions, Kelsen's final work is a mandatory resource for legal and moral philosophers. (shrink)

ABSTRACT: For the Stoics, a syllogism is a formally valid argument; the primary function of their syllogistic is to establish such formal validity. Stoic syllogistic is a system of formal logic that relies on two types of argumental rules: (i) 5 rules (the accounts of the indemonstrables) which determine whether any given argument is an indemonstrable argument, i.e. an elementary syllogism the validity of which is not in need of further demonstration; (ii) one unary and three binary argumental rules which (...) establish the formal validity of non-indemonstrable arguments by analysing them in one or more steps into one or more indemonstrable arguments (cut type rules and antilogism). The function of these rules is to reduce given non-indemonstrable arguments to indemonstrable syllogisms. Moreover, the Stoic method of deduction differs from standard modern ones in that the direction is reversed (similar to tableau methods). The Stoic system may hence be called an argumental reductive system of deduction. In this paper, a reconstruction of this system of logic is presented, and similarities to relevance logic are pointed out. (shrink)

In recent years, several formalisms for program construction have appeared. One such formalism is the type theory developed by Per Martin-L f. Well suited as a theory for program construction, it makes possible the expression of both specifications and programs within the same formalism. Furthermore, the proof rules can be used to derive a correct program from a specification as well as to verify that a given program has a certain property. This book contains a thorough introduction to type theory, (...) with information on polymorphic sets, subsets, monomorphic sets, and a full set of helpful examples. (shrink)

Of all the thinkers of the century of genius that inaugurated modern philosophy, none lived an intellectual life more rich and varied than Gottfried Wilhelm Leibniz. Maria Rosa Antognazza's pioneering biography provides a unified portrait of this unique thinker and the world from which he came. At the centre of the huge range of Leibniz's apparently miscellaneous endeavours, Antognazza reveals a single master project lending unity to his extraordinarily multifaceted life's work. Throughout the vicissitudes of his long life, Leibniz tenaciously (...) pursued the dream of a systematic reform and advancement of all the sciences. As well as tracing the threads of continuity that bound these theoretical and practical activities to this all-embracing plan, this illuminating study also traces these threads back into the intellectual traditions of the Holy Roman Empire in which Leibniz lived and throughout the broader intellectual networks that linked him to patrons in countries as distant as Russia and to correspondents as far afield as China. (shrink)

"Surrender; therefore, surrender or fight" is apparently an argument corresponding to an inference from an imperative to an imperative. Several philosophers, however (Williams 1963; Wedeking 1970; Harrison 1991; Hansen 2008), have denied that imperative inferences exist, arguing that (1) no such inferences occur in everyday life, (2) imperatives cannot be premises or conclusions of inferences because it makes no sense to say, for example, "since surrender" or "it follows that surrender or fight", and (3) distinct imperatives have conflicting permissive presuppositions (...) ("surrender or fight" permits you to fight without surrendering, but "surrender" does not), so issuing distinct imperatives amounts to changing one's mind and thus cannot be construed as making an inference. In response I argue inter alia that, on a reasonable understanding of 'inference', some everyday-life inferences do have imperatives as premises and conclusions, and that issuing imperatives with conflicting permissive presuppositions does not amount to changing one's mind. (shrink)

Of the various accounts of negation that have been offered by logicians in the history of Western logic, that of negation as cancellation is a very distinctive one, quite different from the explosive accounts of modern "classical" and intuitionist logics, and from the accounts offered in standard relevant and paraconsistent logics. Despite its ancient origin, however, a precise understanding of the notion is still wanting. The first half of this paper offers one. Both conceptually and historically, the account of negation (...) as cancellation is intimately connected with connexivist principles such as ¬( ¬). Despite this, standard connexivist logics incorporate quite different accounts of negation. The second half of the paper shows how the cancellation account of negation of the first part gives rise to a semantics for a simple connexivist logic. (shrink)

Prolegomena It is fitting to begin this book on intuitionistic type theory by putting the subject matter into perspective. The purpose of this chapter is to ...

The paper studies the relation between systems of modal logic and systems of consequential implication, a non-material form of implication satisfying "Aristotle's Thesis" (p does not imply not p) and "Weak Boethius' Thesis" (if p implies q, then p does not imply not q). Definitions are given of consequential implication in terms of modal operators and of modal operators in terms of consequential implication. The modal equivalent of "Strong Boethius' Thesis" (that p implies q implies that p does not imply (...) not q) is identified. (shrink)

We present a new proof of soundness/completeness of tableaux with respect to dialogical games in Classical First-Order Logic. As far as we know it is the first thorough result for dialogical games where finiteness of plays is guaranteed by means of what we call repetition ranks.

Three parts of philosophical papers concerned with works, matters and traditions, respectively, present ways of dealing methodically with problems that arise while having and articulating experience. The contents range from philosophy in Antiquity as well as Buddhist to existentialism and analytic philosophy, from relating science and art to the antagonism between freedom and justice. By reflecting on the particular steps of argument the papers become samples of dialogical philosophy with respect both to subject matter and means of procedure.

The constructive reformulation of the semantic theory suggests two basic principles to be assumed: first, the distinction between proper knowledge, expressed in judgemental form, and the assertion conditions for such knowledge; second, ...

Knowledge and Belief An Introduction to the Logic of the Two Notions by Jaakko Hintikka Prepared by Vincent F. Hendricks & John Symons In 1962 Jaakko Hintikka published Knowledge and Belief: An Introduction to the Logic of the Two Notions with Cornell University Press. Almost every paper or a book on epistemic and doxastic logic that has appeared since then has referred to this seminal work. Although many philosophers working in logic, epistemology, game-theory, economics, computer science and linguistics mention the (...) book, it is very likely that most have never literally had their hands on it, much less owned a copy. After a fourth printing in 1969, Knowledge and Belief went out of print and as many of us have found to our dismay, it has become increasingly difficult to find used copies at our local shops or online. It is our pleasure to provide the interdisciplinary community with this reprint edition of Knowledge and Belief. Knowledge and Belief is a classic on which a generation - my generation - of epistemologists cut their teeth. This reissue is welcome. It will provide something for the next generation to chew on. - Fred Dretske, Duke University It is wonderful to see this classic being reissued after so many years out of print. It was extremely influential in its day; its influence continues to this day, through the impact of epistemic logic in fields as diverse distributed computing, artificial intelligence, and game theory. This reissue should make it possible for a new generation of researchers to appreciate Hintikka's groundbreaking work. - Joseph Halpern, Cornell University. (shrink)

We now move to the demonstration of the left-to-right direction of the equivalence result. Let us assume that there is a winning $$\mathbf {P}$$ P -strategy in the dialogical game for $$\varphi $$ φ.

The extensive research in logic conducted by using concepts and methods of game theory as documented in this collection of papers, allows to see dialogue logic in a number of new perspectives. This situation may gain further clarity by looking back to the inception of dialogue logic in the late fifties and early sixties.

Many of the discussions about conditionals can best be put as follows:can those conditionals that involve an entailment relation be formulatedwithin a formal system? The reasons for the failure of the classical approachto entailment have usually been that they ignore the meaning connectionbetween antecedent and consequent in a valid entailment. One of the firsttheories in the history of logic about meaning connection resulted from thestoic discussions on tightening the relation between the If- and the Then-parts of conditionals, which in this (...) context was called. This theory gave a justification for the validity of what we todayexpress through the formulae ¬ and ¬. Hugh MacColl and, more recently, Storrs McCall searched for a formal system in which the validity ofthese formulae could be expressed. Unfortunately neither of the resulting systems is very satisfactory. In this paper we introduce dialogical games with the help of a new connexive If-Then (), the structural rules of which allow the Proponent to develop winning strategies not only for the above-mentioned connexive theses but also for ¬ and ¬. Further on, we developthe corresponding tableau systems and conclude with some remarks on possibleperspectives and consequences of the dialogical approach to connexivity including the loss of uniform substitution leading to a new concept of logical form. (shrink)

Without violating the spirit of Game-Theoretical semantics, its results can be re-worked in Martin-Löf''s Constructive Type Theory by interpreting games as types of Myself''s winning strategies. The philosophical ideas behind Game-Theoretical Semantics in fact highly recommend restricting strategies to effective ones, which is the only controversial step in our interpretation. What is gained, then, is a direct connection between linguistic semantics and computer programming.

Leibniz's well-known thesis that the actual world is just one among many possible worlds relies on the claim that some possibles are incompossible , meaning that they cannot belong to the same world. Notwithstanding its central role in Leibniz's philosophy, commentators have disagreed about how to understand the compossibility relation. We examine several influential interpretations and demonstrate their shortcomings. We then sketch a new reading, the cosmological interpretation, and argue that it accommodates two key conditions that any successful interpretation must (...) satisfy. (shrink)

Nous montrons dans cet article comment les approches dynamiques en logique contemporaine ont retrouvé, quoique sous d ’ autres attendus, une configuration théorique qu ’ on peut attribuer à Aristote au moment de la rédaction des Topiques. Dans cette configuration, la logique et la rhétorique – ou au moins la dialectique – se complètent dans le cadre conceptuel homogène offert par la dialectique, entendue comme une certaine forme relativement codifiée de débat critique. L ’ idée principale est qu ’ aujourd (...) ’ hui, de même qu ’ alors, la dialectique est le cadre dans lequel il est possible de penser le rapport entre la logique et les formes générales de l ’ argumentation d ’ une part, et entre la logique et la théorie de la connaissance scientifique d ’ autre part. (shrink)

The paper discusses ten philosophical problems in deontic logic: how to formally represent norms, when a set of norms may be termed ‘coherent’, how to deal with normative conflicts, how contraryto-duty obligations can be appropriately modeled, how dyadic deontic operators may be redefined to relate to sets of norms instead of preference relations between possible worlds, how various concepts of permission can be accommodated, how meaning postulates and counts-as conditionals can be taken into account, and how sets of norms may (...) be revised and merged. The problems are discussed from the viewpoint of input/output logic as developed by van der Torre & Makinson. We argue that norms, not ideality, should take the central position in deontic semantics, and that a semantics that represents norms, as input/output logic does, provides helpful tools for analyzing, clarifying and solving the problems of deontic logic. (shrink)

In this paper my objective is two-fold. First, I will try to provide further arguments in favour of the view defended in my earlier paper¹. In particular, I will try to show (in § 1) that a plausible understanding of the notion of a complete concept, coupled with (what I take to be) a reasonable interpretation of Leibniz's intriguing talk of severa “possible Adams” (§ 2), leads quite naturally to the view that Leibniz was committed to the doctrine of world-bound (...) individuals. Second, I will try to show (in § 3) that a suggestive way of saving contingency in the framework of Leibniz's theory of complete concepts is bound to fail : and the reasons for this failure will provide further evidence in favour of the view under present discussion. The remaining sections of the paper (§§ 4-6), will be concerned with fixing and making precise some of the loose ends of the previous three sections. Thus §§ 4 and 5 will be devoted to an analysis of Leibniz's use and understanding of the notions of contingency and necessity, and essence and accident, respectively. It will be shown that Leibniz's use and understanding of those notions is perfectly consistent with his commitment to the doctrine of world-bound individuals. In § 6, finally, I will try to indicate exactly how David Lewis' Counterpart Theory can be brought to bear upon Leibniz's theory of complete concepts, and, specifically, how it ought to be interpreted in that context. (shrink)

Gottfried Wilhelm Leibniz was an outstanding contributor to many fields of human knowledge. The historiography of philosophy has tagged him as a “rationalist”. But what does this exactly mean? Is he a “rationalist” in the same sense in Mathematics and Politics, in Physics and Jurisprudence, in Metaphysics and Theology, in Logic and Linguistics, in Technology and Medicine, in Epistemology and Ethics? What are the most significant features of his “rationalism”, whatever it is? For the first time an outstanding group of (...) Leibniz researchers, some acknowledged as leading scholars, others in the beginning of a promising career, who specialize in the most significant areas of Leibniz’s contributions to human thought and action, were requested to spell out the nature of his rationalism in each of these areas, with a view to provide a comprehensive picture of what it amounts to, both in its general drive and in its specific features and eventual inner tensions. The chapters of the book are the result of intense discussion in the course of an international conference focused on the title question of this book, and were selected in view of their contribution to this topic. They are clustered in thematically organized parts. No effort has been made to hide the controversies underlying the different interpretations of Leibniz’s “rationalism” – in each particular domain and as a whole. On the contrary, the editor firmly believes that only through a variety of conflicting interpretive perspectives can the multi-faceted nature of an oeuvre of such a magnitude and variety as Leibniz’s be brought to light and understood as it deserves. (shrink)

Abstract.If norms are neither true nor false, can logical relations such as contradiction and entailment obtain between them? Earlier logical positivists and also Hans Kelsen in his later years have answered the question with No. While appreciating the seriousness of the problem, the author of the present paper makes a fresh attempt to answer the question with Yes. His answer presupposes that norms can be judged from the point of view of their rationality. The deontic loic or logic of norms (...) built on this foundation is much more restricted, however, than tae “classical” systems. This again is a consequence of the author's opinion that the sentential connectives (negation, conjunction, disjunction, etc.) apply to norms only on condition that they can be “shifted” from joining norm‐formulations to the descriptive contents of the norms themselves. (shrink)

Nous présentons ici une version modale des dialogues de recherche de conditions (SSD) que nous avons introduits dans [Rahman & Keiff 2004]. La sémantique utilisée correspond à celle des systèmes modaux non normaux.

The main aim of our paper is to implement Leibniz's analysis of the conditional right in the framework of a dialogical approach to Public Announcement Logic. According to our view, on one hand: PAL furnishes a dynamic epistemic operator which models communication exchange between different agents that seems to be very close to Leibniz understanding of the dynamics between the truth of a proposition and the knowledge of the truth of that proposition (Leibniz calls the latter certification of its truth); (...) on the other hand, the dialogical approach provides a semantics for the dynamic epistemic operator in the context of conditional right by means of which: (i) the exchange between agents leading to a public announcement amounts to the (contractual) interaction of commitments of both the benefactor and the beneficiary of a conditional right (ii) the notion of certification is understood as an action, namely as a move where the beneficiary asks the benefactor to stand to his commitments, (iii) some restrictions specific to the logical nature of the head and the tail of the conditional right can be implemented by combining PAL with some features of linear logic within the same theory of meaning. (shrink)

RésuméLa définition de la condition suspensive, telle qu’elle nous est donnée dans l’article 1181 du Code civil français, est aujourd’hui au centre de différents projets de réforme. Si aucun projet de réforme n’a réussi à emporter l’assentiment de tous les juristes, nombre d’entre eux semblent s’accorder sur la nécessité de réformer ce texte—inchangé depuis 1804. Pourquoi un tel consensus sur ce besoin de réécriture de la définition de la condition suspensive mène à une discussion doctrinale où deux positions principales s’opposent? (...) C’est à cette question que nous tâchons de répondre en traquant l’origine de cette scission dans la lettre même du texte dont nous analysons à la fois la structure logique et la signification des termes employés pour sa rédaction. Cette analyse nous permet de mettre en évidence la sémantique ambiguë du terme “incertain”, terme pour lequel nous proposons une analyse logique de sa signification que nous comparons ensuite à celle du terme “inconnu”. (shrink)

ABSTRACT: Summary presentation of the surviving logic theories of Philo the Dialectician (aka Philo of Megara) and Diodorus Cronus, including some general remarks on propositional logical elements in their logic, a presentation of their theories of the conditional and a presentation of their modal theories, including a brief suggestion for a solution of the Master Argument.