A common reaction to Hegel’s suggestion that we collapse Kant’s distinction between form and content is that, since such a move would also deprive us of any way of distinguishing the merely logical from the real possibility of our concepts, it is incoherent and ought to be rejected. It is true that these two distinctions are intimately related in Kant, such that if one goes, the other does as well. But it is less obvious that giving them up as Kant (...) conceives them is as incoherent a proposal as many of Hegel’s critics think. It has been the point of a recent account of Hegel’s idealism to demonstrate that his critique of Kant’s dichotomy between form and content or concept and intuition does not commit him to the view that human cognition is materially creative of its content in the manner of a God-like or intuitive intellect—does not, in other words, signify a return to a pre-Critical metaphysics. This is the interpretative stance I adopt here as well, in hope of giving defenders of Kant reasons for taking Hegel more seriously. (shrink)

The First International Workshop brings together researchers from the theoretical ends of the logic programming and artificial intelligence communities to discuss their mutual interests. Logic programming deals with the use of models of mathematical logic as a way of programming computers, where theoretical AI deals with abstract issues in modeling and representing human knowledge and beliefs. One common ground is nonmonotonic reasoning, a family of logics that includes room for the kinds of variations that can be found (...) in human reasoning. Topics covered: Stable Semantics. Default Logic. AutoEpistemic Logic. Truth Maintenance Systems. Implementation Issues. Diagnosis. Applications. Inheritance Reasoning. Logics of Belief. Inconsistency and Non-Monotonicity. (shrink)

The paper surveys the currently available axiomatizations of common belief (CB) and common knowledge (CK) by means of modal propositional logics. (Throughout, knowledge- whether individual or common- is defined as true belief.) Section 1 introduces the formal method of axiomatization followed by epistemic logicians, especially the syntax-semantics distinction, and the notion of a soundness and completeness theorem. Section 2 explains the syntactical concepts, while briefly discussing their motivations. Two standard semantic constructions, Kripke structures and neighbourhood structures, are introduced in Sections (...) 3 and 4, respectively. It is recalled that Aumann's partitional model of CK is a particular case of a definition in terms of Kripke structures. The paper also restates the well-known fact that Kripke structures can be regarded as particular cases of neighbourhood structures. Section 3 reviews the soundness and completeness theorems proved w.r.t. the former structures by Fagin, Halpern, Moses and Vardi, as well as related results by Lismont. Section 4 reviews the corresponding theorems derived w.r.t. the latter structures by Lismont and Mongin. A general conclusion of the paper is that the axiomatization of CB does not require as strong systems of individual belief as was originally thought- only monotonicity has thusfar proved indispensable. Section 5 explains another consequence of general relevance: despite the "infinitary" nature of CB, the axiom systems of this paper admit of effective decision procedures, i.e., they are decidable in the logician's sense. (shrink)

The notions of common knowledge or common belief play an important role in several areas of computer science , in philosophy, game theory, artificial intelligence, psychology and many other fields which deal with the interaction within a group of “agents”, agreement or coordinated actions. In the following we will present several deductive systems for common knowledge above epistemic logics –such as K, T, S4 and S5 –with a fixed number of agents. We focus on structural and proof-theoretic properties of these (...) calculi. (shrink)

We investigate an axiomatization of the notion of common belief that makes use of no rules of inference and highlight the property of the set of accessibility relations that characterizes each axiom.

Anil Gupta's slightly revised 1977 Pittsburgh doctoral dissertation is not a linguistic investigation of common nouns. There is no thorough attempt to organize and explain data about common nouns in natural languages. Gupta's goal is to develop and to defend formal modal languages and logics useful for the representation and defense of metaphysical theses on topics such as the structure of individuals, sorts or kinds, substances, and essences. He does, however, develop the special features of his formal syntax and semantics (...) on the basis of two theses about common nouns in our natural languages. Geach's work suggests the first thesis that properly expressed identity statements are of the form: b is the same K as c, where K is a common noun. Because the individual variables bound by quantifiers must be capable of being terms of an identity relation, this first thesis leads Gupta to require quantifiers to link individual variables with common noun expressions. Thus in his formal languages we can only express: "every K is _____" or "some K is _____" where K is syntactically part of the quantifier. We can call this "sortal quantification." Hence, "Every K is P" and "Some K is P" are not even expressible as "If anything is K then it is P" or "Something is K and P," let alone equivalent to such ill-formed expressions in his languages. Gupta's book is a useful introduction to the syntax and semantics for languages with this non-standard sortal quantification for those already familiar with the syntax and formal semantics of first order extensional and modal languages with standard quantifiers. Those unfamiliar with standard formal languages and model structure semantics will find Gupta's provocative metaphysical theories and conjectures inaccessible. (shrink)

We show that several logics of common belief and common knowledge are not only complete, but also strongly complete, hence compact. These logics involve a weakened monotonicity axiom, and no other restriction on individual belief. The semantics is of the ordinary fixed-point type.

This book suggests a bold comparative approach to broad cultural differences between Africa and Melanesia. Its theme is personhood, understood in terms of what anthropologists call embodiment. These concepts are applied to questions ranging from the meanings of spirit possession, to the logics of witchcraft and kinship relations, the use of rituals in healing, and even the impact of capitalism. Questioning common assumptions about the huge differences among these discrete areas, the contributions document surprising continuities.

The essay is a written version of a talk Nakamura Yūjirō gave at the College international de philosophie in Paris in 1983. In the talk Nakamura connects the issue of common sense in his own work to that of place in Nishida Kitarō and the creative imagination in Miki Kiyoshi. He presents this connection between the notions of common sense, imagination, and place as constituting one important thread in contemporary Japanese philosophy. He begins by discussing the significance of place (basho) (...) that is being rediscovered today in response to the shortcomings of the modern Western paradigm, and discusses it in its various senses, such as ontological ground or substratum, the body, symbolic space, and linguistic or discursive topos in ancient rhetoric. He then relates this issue to the philosophy of place Nishida developed in the late 1920s, and after providing an explication of Nishida’s theory, discusses it further in light of some linguistic and psychological theories. Nakamura goes on to discuss his own interest in the notion of common sense traceable to Aristotle and its connection to the rhetorical concept of topos, and Miki’s development of the notion of the imagination in the 1930s in response to Nishida’s theory. And in doing so he ties all three—common sense, place, and imagination—together as suggestive of an alternative to the modern Cartesian standpoint of the rational subject that has constituted the traditional paradigm of the modern West. (shrink)

We present a cut-free tableau calculus with histories and variables for the EXPTIME-complete multi-modal logic of common knowledge. Our calculus constructs the tableau using only one pass, so proof-search for testing theoremhood of ϕ does not exhibit the worst-case EXPTIME-behaviour for all ϕ as in two-pass methods. Our calculus also does not contain a “finitized ω-rule” so that it detects cyclic branches as soon as they arise rather than by worst-case exponential branching with respect to the size of ϕ. (...) Moreover, by retaining the rooted-tree form from traditional tableaux, our calculus becomes amenable to the vast array of optimisation techniques which have proved essential for “practical” automated reasoning in very expressive description logics. Our calculus forms the basis for developing a uniform framework for the family of all fix-point logics of common knowledge. However, there is still no “free lunch” as, in the worst case, our method exhibits 2EXPTIME-behaviour. A prototype implementation can be found at twb.rsise.anu.edu.au which allows users to test formulae via a simple graphical interface. (shrink)

The essay is a written version of a talk Nakamura Yūjirō gave at the Collège international de philosophie in Paris in 1983. In the talk Nakamura connects the issue of common sense in his own work to that of place in Nishida Kitarō and the creative imagination in Miki Kiyoshi. He presents this connection between the notions of common sense, imagination, and place as constituting one important thread in contemporary Japanese philosophy. He begins by discussing the significance of place (basho) (...) that is being rediscovered today in response to the shortcomings of the modern Western paradigm, and discusses it in its various senses, such as ontological ground or substratum, the body, symbolic space, and linguistic or discursive topos in ancient rhetoric. He then relates this issue to the philosophy of place Nishida developed in the late 1920s, and after providing an explication of Nishida’s theory, discusses it further in light of some linguistic and psychological theories. Nakamura goes on to discuss his own interest in the notion of common sense traceable to Aristotle and its connection to the rhetorical concept of topos, and Miki’s development of the notion of the imagination in the 1930s in response to Nishida’s theory. And in doing so he ties all three—common sense, place, and imagination—together as suggestive of an alternative to the modern Cartesian standpoint of the rational subject that has constituted the traditional paradigm of the modern West. (shrink)

In terms of formal deductive systems and multi-dimensional Kripke frames we study logical operations know, informed, common knowledge and common information. Based on [6] we introduce formal axiomatic systems for common information logics and prove that these systems are sound and complete. Analyzing the common information operation we show that it can be understood as greatest open fixed points for knowledge formulas. Using obtained results we explore monotonicity, omniscience problem, and inward monotonocity, describe their connections and give dividing examples. Also (...) we find algorithms recognizing these properties for some particular cases. (shrink)

Gupta's book [9] contains a theory of modal logic that is closely related to my modal language ML v [2], and his theory is used to treat some interesting philosophical problems. Hence, it is natural for me to review this valuable book and to concentrate on its logics, the more so as its use has already been spoken of and appreciated by Kapitan [10], although I cannot but share his appreciation.

The logic of common belief does not always reflect that of individual beliefs. In particular, even when the individual belief operators satisfy the KD45 logic, the common belief operator may fail to satisfy axiom 5. That is, it can happen that neither is A commonly believed nor is it common belief that A is not commonly believed. We identify the intersubjective restrictions on individual beliefs that are incorporated in axiom 5 for common belief.

For the modal logic |$\textsf {S4}^{C}_{I}$|⁠, we identify the class of completable |$\textsf {S4}^{C}_{I}$|-algebras and prove for them a Stone-type representation theorem. As a consequence, we obtain strong algebraic and topological completeness of the logic |$\textsf {S4}^{C}_{I}$| in the case of local semantic consequence relations. In addition, we consider an extension of the logic |$\textsf {S4}^{C}_{I}$| with certain infinitary derivations and establish the corresponding strong completeness results for the enriched system in the case of global semantic consequence (...) relations. (shrink)

Perfect for students with no background in logic or philosophy, Simple Formal Logic provides a full system of logic adequate to handle everyday and philosophical reasoning. By keeping out artificial techniques that aren’t natural to our everyday thinking process, Simple Formal Logic trains students to think through formal logical arguments for themselves, ingraining in them the habits of sound reasoning. Simple Formal Logic features: a companion website with abundant exercise worksheets, study supplements (including flashcards for (...) symbolizations and for deduction rules), and instructor’s manual two levels of exercises for beginning and more advanced students a glossary of terms, abbreviations and symbols. This book arose out of a popular course that the author has taught to all types of undergraduate students at Loyola University Chicago. He teaches formal logic without the artificial methods–methods that often seek to solve farfetched logical problems without any connection to everyday and philosophical argumentation. The result is a book that teaches easy and more intuitive ways of grappling with formal logic–and is intended as a rigorous yet easy-to-follow first course in logical thinking for philosophy majors and non-philosophy majors alike. (shrink)

In order to capture the concept of common knowledge, various extensions of multi-modal epistemic logics, such as fixed-point ones and infinitary ones, have been proposed. Although we have now a good list of such proposed extensions, the relationships among them are still unclear. The purpose of this paper is to draw a map showing the relationships among them. In the propositional case, these extensions turn out to be all Kripke complete and can be comparable in a meaningful manner. F. Wolter (...) showed that the predicate extension of the Halpern-Moses fixed-point type common knowledge logic is Kripke incomplete. However, if we go further to an infinitary extension, Kripke completeness would be recovered. Thus there is some gap in the predicate case. In drawing the map, we focus on what is happening around the gap in the predicate case. The map enables us to better understand the common knowledge logics as a whole. (shrink)

In _On The Soul_ (425a-b), Aristotle drew a distinction between those qualities that are perceptible only via a single sense and those that are perceptible by more than one. The latter qualities he called.

The logical structure of quantum gravity is addressed in the framework of the so-called manifestly covariant approach. This permits to display its close analogy with the logics of quantum mechanics. More precisely, in QG the conventional 2-way principle of non-contradiction holding in Classical Mechanics is shown to be replaced by a 3-way principle. The third state of logical truth corresponds to quantum indeterminacy/undecidability, i.e., the occurrence of quantum observables with infinite standard deviation. The same principle coincides, incidentally, with the earlier (...) one shown to hold in Part I, in analogous circumstances, for QM. However, this conclusion is found to apply only provided a well-defined manifestly-covariant theory of the gravitational field is adopted both at the classical and quantum levels. Such a choice is crucial. In fact it makes possible the canonical quantization of the underlying unconstrained Hamiltonian structure of general relativity, according to an approach recently developed by Cremaschini and Tessarotto. Remarkably, in the semiclassical limit of the theory, Classical Logic is proved to be correctly restored, together with the validity of the conventional 2-way principle. (shrink)

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)

One of the most challenging and fascinating issue in mathematical and theoretical physics concerns the possibility of identifying the logic underlying the so-called quantum universe, i.e., Quantum Mechanics and Quantum Gravity. Besides the sheer difficulty of the problem, inherent in the actual formulation of Quantum Mechanics—and especially of Quantum Gravity—to be used for such a task, a crucial aspect lies in the identification of the appropriate axiomatic logical proposition calculus to be associated to such theories. In this paper the (...) issue of the validity of the conventional principle of non-contradiction is called into question and is investigated in the context of non-relativistic Quantum Mechanics. In the same framework a modified form of the principle, denoted as 3-way PNC is shown to apply, which relates the axioms of quantum logic with the physical requirements placed by the Heisenberg Indeterminacy Principle. (shrink)

Common nouns enter into modern predicate logic only as parts of predicates, While in lesniewski's 'ontology' they are classified together with proper nouns as 'names'. A system of natural deduction rules is presented which sharply separates proper from common nouns, Within which lesniewski's calculus is contained as a logic solely of common nouns, Together with copula, Identity predicate, Definite article, And quantifiers 'any', 'every', 'some' and 'no'. The fragment developed is closer to the natural syntax of english than (...) either frege's or lesniewski's languages, Enabling these to be seen as complementary rather than competing, As approximations to syntactically more complex languages. (shrink)

Abstract In this essay, I critically discuss a theory of utterance content and de re communication that Anne Bezuidenhout has recently developed in a series of articles. This theory regards the significance of utterances as more pragmatic in nature than allowed by traditional accounts; further, it downplays logical considerations in explaining de re communication, choosing instead to emphasize its psychological character. Included among the implications of this approach is the rejection of what can be called ?common content?, or utterance content (...) that is held in common by speaker and listener. After describing this theory, I argue that Bezuidenhout does not supply a compelling reason to prefer her account of utterance content over more traditional alternatives that make room for elements of content held in common between speaker and listener. Further, I argue that her account of de re communication supplies even more reason to reject the view of content to which she subscribes. In the end, it will be clear that she has no principled reason for rejecting common content. (shrink)

This new and expanded edition of The Logic of Real Arguments explains a distinctive method for analysing and evaluating arguments. It discusses many examples, ranging from newspaper articles to extracts from classic texts, and from easy passages to much more difficult ones. It shows students how to use the question 'What argument or evidence would justify me in believing P?', and also how to deal with suppositional arguments beginning with the phrase 'Suppose that X were the case.' It aims (...) to help students to think critically about the kind of sustained, theoretical arguments which they commonly encounter in the course of their studies, including arguments about the natural world, about society, about policy, and about philosophy. It will be valuable for students and their teachers in a wide range of disciplines including philosophy, law and the social sciences. (shrink)

Current dynamic epistemic logics for analyzing effects of informational events often become cumbersome and opaque when common knowledge is added for groups of agents. Still, postconditions involving common knowledge are essential to successful multi-agent communication. We propose new systems that extend the epistemic base language with a new notion of ‘relativized common knowledge’, in such a way that the resulting full dynamic logic of information flow allows for a compositional analysis of all epistemic postconditions via perspicuous ‘reduction axioms’. We (...) also show how such systems can deal with factual alteration, rather than just information change, making them cover a much wider range of realistic events. After a warm-up stage of analyzing logics for public announcements, our main technical results are expressivity and completeness theorems for a much richer logic that we call LCC. This is a dynamic epistemic logic whose static base is propositional dynamic logic (PDL), interpreted epistemically. This system is capable of expressing all model-shifting operations with finite action models, while providing a compositional analysis for a wide range of informational events. This makes LCC a serious candidate for a standard in dynamic epistemic logic, as we illustrate by analyzing some complex communication scenarios, including sending successive emails with both ‘cc’ and ‘bcc’ lines, and other private announcements to subgroups. Our proofs involve standard modal techniques, combined with a new application of Kleene’s theorem on finite automata, as well as new Ehrenfeucht games of model comparison. (shrink)

No mathematical background is necessary to appreciate this classic of probability theory, which remains unsurpassed in its clarity, readability, and sheer charm. Its author, British logician John Venn (1834-1923), popularized the famous Venn Diagrams that are commonly used in teaching elementary mathematics.

Theories of epistemic justification are commonly assessed by exploring their predictions about particular hypothetical cases – predictions as to whether justification is present or absent in this or that case. With a few exceptions, it is much less common for theories of epistemic justification to be assessed by exploring their predictions about logical principles. The exceptions are a handful of ‘closure’ principles, which have received a lot of attention, and which certain theories of justification are well known to invalidate. But (...) these closure principles are only a small sample of the logical principles that we might consider. In this paper, I will outline four further logical principles that plausibly hold for justification and two which plausibly do not. While my primary aim is just to put these principles forward, I will use them to evaluate some different approaches to justification and (tentatively) conclude that a ‘normic’ theory of justification best captures its logic. (shrink)

Imagination has received a great deal of attention in different fields such as psychology, philosophy and the cognitive sciences, in which some works provide a detailed account of the mechanisms involved in the creation and elaboration of imaginary worlds. Although imagination has also been formalized using different logical systems, none of them captures those dynamic mechanisms. In this work, we take inspiration from the Common Frame for Imagination Acts, that identifies the different processes involved in the creation of imaginary worlds, (...) and we use it to define a dynamic formal system called the Logic of Imagination Acts. We build our logic by using a possible-worlds semantics, together with a new set of static and dynamic modal operators. The role of the new dynamic operators is to call different algorithms that encode how the formal model is expanded in order to capture the different mechanisms involved in the creation and development of imaginary worlds. We provide the definitions of the language, the semantics and the algorithms, together with an example that shows how the model is expanded. By the end, we discuss some interesting features of our system, and we point out to possible lines of future work. (shrink)

This new and expanded edition of The Logic of Real Arguments explains a distinctive method for analysing and evaluating arguments. It discusses many examples, ranging from newspaper articles to extracts from classic texts, and from easy passages to much more difficult ones. It shows students how to use the question 'What argument or evidence would justify me in believing P?', and also how to deal with suppositional arguments beginning with the phrase 'Suppose that X were the case.' It aims (...) to help students to think critically about the kind of sustained, theoretical arguments which they commonly encounter in the course of their studies, including arguments about the natural world, about society, about policy, and about philosophy. It will be valuable for students and their teachers in a wide range of disciplines including philosophy, law and the social sciences. (shrink)

This new and expanded edition of The Logic of Real Arguments explains a distinctive method for analysing and evaluating arguments. It discusses many examples, ranging from newspaper articles to extracts from classic texts, and from easy passages to much more difficult ones. It shows students how to use the question 'What argument or evidence would justify me in believing P?', and also how to deal with suppositional arguments beginning with the phrase 'Suppose that X were the case.' It aims (...) to help students to think critically about the kind of sustained, theoretical arguments which they commonly encounter in the course of their studies, including arguments about the natural world, about society, about policy, and about philosophy. It will be valuable for students and their teachers in a wide range of disciplines including philosophy, law and the social sciences. (shrink)

Imagination has received a great deal of attention in different fields such as psychology, philosophy and the cognitive sciences, in which some works provide a detailed account of the mechanisms involved in the creation and elaboration of imaginary worlds. Although imagination has also been formalized using different logical systems, none of them captures those dynamic mechanisms. In this work, we take inspiration from the Common Frame for Imagination Acts, that identifies the different processes involved in the creation of imaginary worlds, (...) and we use it to define a dynamic formal system called the Logic of Imagination Acts. We build our logic by using a possible-worlds semantics, together with a new set of static and dynamic modal operators. The role of the new dynamic operators is to call different algorithms that encode how the formal model is expanded in order to capture the different mechanisms involved in the creation and development of imaginary worlds. We provide the definitions of the language, the semantics and the algorithms, together with an example that shows how the model is expanded. By the end, we discuss some interesting features of our system, and we point out to possible lines of future work. (shrink)