Modules allow the reuse of an ontology as part of another ontology. If the ontologies do not share a common domain of discourse a simple ‘cut and paste’ approach to module reuse leads to unintended...

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)

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)

At the onset of quantum mechanics, it was argued that the new theory would entail a rejection of classical logic. The main arguments to support this claim come from the non-commutativity of quantum observables, which allegedly would generate a non-distributive lattice of propositions, and from quantum superpositions, which would entail new rules for quantum disjunctions. While the quantum logic program is not as popular as it once was, a crucial question remains unsettled: what is the relationship between the (...) logical structures of classical and quantum mechanics? In this essay we answer this question by showing that the original arguments promoting quantum logic contain serious flaws, and that quantum theory does satisfy the classical distributivity law once the full meaning of quantum propositions is properly taken into account. Moreover, we show that quantum mechanics can generate a distributive lattice of propositions, which, unlike the one of quantum logic, includes statements about expectation values which are of undoubtable physical interest. Lastly, we show that the lattice of statistical propositions in classical mechanics follows the same structure, yielding an analogue non-commutative sublattice of classical propositions. This fact entails that the purported difference between classical and quantum logic stems from a misconstructed parallel between the two theories. (shrink)

This cumulative course on Johannes Heinrichs' philosophical works presents the essence of his previous publications: A rich, consistent, and novel monolithic system defying temptations by the zeitgeist. Starting with an emphasis on reflection as the basis of epistemology, Heinrichs also covers the mind-body dualism in an anthropology chapter, moves on to presenting summaries of his 'Theory of Democracy' as well as of his 'Philosophical Semiotics', followed by an outline of structural and integral ontology. An overview of ethical positions in the (...) final chapter proves the fertility of Heinrichs? theoretical-reflection methods. (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)

Hegel's logic is often understood as a competitor to ordinary formal logic; this leads to such false accusations as that hegel "denies the principle of non-Contradiction." on the contrary, Hegel's speculative logic is wholly conservative with respect to ordinary logic. What hegel denies is ordinary logic's suitability to be a paradigm for philosophy. Hegel's logic, Itself, Can be seen as arising from a critical ontological reflection on ordinary logic.

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.

Antoine Arnauld and Pierre Nicole were philosophers and theologians associated with Port-Royal Abbey, a centre of the Catholic Jansenist movement in seventeenth-century France. Their enormously influential Logic or the Art of Thinking, which went through five editions in their lifetimes, treats topics in logic, language, theory of knowledge and metaphysics, and also articulates the response of 'heretical' Jansenist Catholicism to orthodox Catholic and Protestant views on grace, free will and the sacraments. In attempting to combine the categorical theory (...) of the proposition with a Cartesian account of knowledge, their Logic represents the classical view of judgment which inspired the modern transformation in logic and semantic theory by Frege, Russell, Wittgenstein and recent philosophers. This edition presents a new translation of the text, together with a historical introduction and suggestions for further reading. (shrink)

We show the faithful embedding of common knowledge logic CKL into game logic GL, that is, CKL is embedded into GL and GL is a conservative extension of the fragment obtained by this embedding. Then many results in GL are available in CKL, and vice versa. For example, an epistemic consideration of Nash equilibrium for a game with pure strategies in GL is carried over to CKL. Another important application is to obtain a Gentzen-style sequent calculus formulation (...) of CKL and its cut-elimination. The faithful embedding theorem is proved for the KD4-type propositional CKL and GL, but it holds for some variants of them. (shrink)

In this paper, we will explore two initiatives that focus on the importance of employing logical theories in educating people how to think and reason properly, one in Poland: The Lvov-Warsaw School; the other in North America: The Informal Logic Initiative. These two movements differ in the logical means and skills that they focus on. However, we believe that they share a common purpose: to educate students in logic and reasoning (logical education conceived as a process) so (...) that they may be able to apply their skills to analyze the issues in their society (logical culture as a result of logical education). The aim of the paper is to justify this claim by exploring research objectives and products that are common to both movements. (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)

Two approaches for defining common knowledge coexist in the literature: the infinite iteration definition and the circular or fixed point one. In particular, an original modelization of the fixed point definition was proposed by Barwise in the context of a non-well-founded set theory and the infinite iteration approach has been technically analyzed within multi-modal epistemic logic using neighbourhood semantics by Lismont. This paper exhibits a relation between these two ways of modelling common knowledge which seem at first (...) quite different. (shrink)

Current dynamic epistemic logics often become cumbersome and opaque when common knowledge is added for groups of agents. Still, postconditions regarding common knowledge express the essence of what communication achieves. We present some methods that yield so-called reduction axioms for common knowledge. We investigate the expressive power of public announcement logic with relativized common knowledge, and present reduction axioms that give a detailed account of the dynamics of common knowledge in some major communication types.

Current dynamic epistemic logics often become cumbersome and opaque when common knowledge is added for groups of agents. Still, postconditions regarding common knowledge express the essence of what communication achieves. We present some methods that yield so-called reduction axioms for common knowledge. We investigate the expressive power of public announcement logic with relativized common knowledge, and present reduction axioms that give a detailed account of the dynamics of common knowledge in some major communication types.

This paper is about the efforts the norwegian psychologist Jan Smedslund made in analyzing and checking philosophically his theory called ‘Psycho-logic’. I am going to reconstruct and discuss the debates between Smedslund and several critics, which have been going on since about 1978, mainly in the “Scandinavian Journal of Psychology”. A result will be that the kind of modal logics Smedslund uses — a type with realistic semantics and epistemology — is not the proper one for the analysis of (...) ‘Psycho-logic’. (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)

Logic, considered as a technical discipline inaugurated by Aristotle and typically represented by the variety of the modern logical calculi, constitutes a clarification and refinement of a conviction and practice present in common sense, that is, the fact that humans believe that truth can be acquired not only by immediate evidence, but also by means of arguments. As a first step logic can be seen as a “descriptive” record of the main forms of the arguments present in (...) common sense, but the fact that some of these patterns can actually allow for the derivation of false consequences from true premises imposes the task of making explicit what patterns correspond to a “correct reasoning” and what not. At this point logic appears endowed with a “normative” characteristic. This amounts to saying that logical calculi are intended to adequately mirror the intuitive notion of “logical consequence” and in this sense they cannot be totally arbitrary or conventional, but must satisfy certain basic requirements such as the conditions of soundness and of semantic completeness. In such a way they are “judged” according to the fundamental requirements present at the level of common sense and appear as “idealizations” of the kinds of reasoning practiced in common sense. For this reason also several kinds of logical calculi are fully justified since they make explicit in an idealized form the concrete ways of reasoning that are imposed by the particular domain of reference of the discipline in which they are used and which are basically recognized in common sense. (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)

The paper deals with a type of whole and part that can be found in Aquinas’ work and to which no attention has been paid so far. This type of whole and part can be called metaphysical whole and metaphysical part, respectively. In the paper, metaphysical whole and part are put forth on the problem of the logical and metaphysical structure of a common nature.

This paper examines Hegel’s accounts of the nature of judgements and inferences in the ‘subjective logic’ of the Science of Logic, and does so in light of the history of the tradition of formal logic to his time. It is argued that, contrary to the attitude often displayed by interpreters of Hegel’s logic, it is important to understand the positive role played by formal logic, ‘logic commonly so called’, in Hegel’s own conception of (...) class='Hi'>logic. It is argued that Hegel’s own scientific presentation [Darstellung] of logic relies on a dialectic working through the tradition of formal logic from Aristotle to Leibniz. The positions within the dialectic are most easily brought into focus in terms of the distinction between Aristotelian and Stoic logic, but they can also be seen as internal to Aristotelian logic. The logical tradition can be regarded as presenting a type of reductio ad absurdum, and a science of logic must examine what it was about Aristotle’s original project that brought it to this fate. (shrink)

In this paper, I situate Logical Argument Mapping within.

In this paper we investigate first order common knowledge logics; i.e., modal epistemic logics based on first order logic with common knowledge operators. It is shown that even rather weak fragments of first order common knowledge logics are not recursively axiomatizable. This applies, for example, to fragments which allow to reason about names only; that is to say, fragments the first order part of which is based on constant symbols and the equality symbol only. Then formal (...) properties of "quantifying into" epistemic contexts are investigated. The results are illustrated by means of epistemic representations of Nash Equilibria for finite games with mixed strategies. (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.

For almost 300 years, five different art forms have used the same instructional method. This Common Arts Instructional Method (CAIM) can be explained using a variety of theories. The CAIM also offers the opportunity to understand instructional methods under the banner of design: instances of types rather than applications of laws or principles. The differences between theory and design are explored, and some recommendations are offered for striking new instances of this common type.

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)

Unlike statutory law, which relies on the explicit formulation of rules, common law is thought to emerge from a complex doctrine of precedential constraint, according to which decisions in earlier cases constrain later courts while still allowing these courts the freedom to address new situations in creative ways. Although this doctrine is applied by legal practitioners on a daily basis, it has proved to be considerably more difficult to develop an adequate theoretical account of the doctrine itself. Drawing on (...) recent work in legal theory, as well as AI and law, this book develops a new account of precedential constraint and the balance achieved in the common law between constraint and freedom. This account, which involves construction of a group priority ordering among reasons, is then applied to other topics including the semantics of open-textured predicates and the practice of making exceptions to general rules. (shrink)

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)

For thirty years at least, I have designated myself as a zoologist interested in the “philosophical aspects of biology”. But I have now to admit that not until within the last two or three years have I recognized that logic, particularly in its inductive aspect, is involved in such interest.For me as a zoologist with a predilection for natural history, observation has had a place of wide application and of implicit confidence. Until recently, I had rested in the supposition (...) that after all of the devices practiced by naturalists to insure certainty of their observations, nothing further was needed so far as the information and understanding they gained was concerned. I had gone ahead with my reasoning, my logic, with no more qualms about the trustworthiness of the “inductive” than of the “deductive” side of it. I had not taken seriously the assertion, made years ago in my hearing by an eminent philosopher, that no one can be a philosopher without being skeptical and critical of the use of his senses in getting knowledge. Latterly, however, I have come to see that traditional philosophers take themselves very seriously in such assertions. This realization has been due to the discovery that the recent advances in physics and mathematics have led most of the leaders in these fields to believe that observation and the inductive side of logic may be left where they were a hundred years ago. These scientists seem to be about where John Stuart Mill was in his effort to improve Lord Bacon's effort for a better understanding of both observation and induction. (shrink)

The least common subsumer of a set of concept descriptions is the most specific concept description that subsumes all of the concept descriptions in the given set. By computing the lcs, commonalities between concept descriptions can be made explicit. This is an important inference task useful in several applications, including, for instance, the bottom-up construction of description logic knowledge bases. Previous work on the lcs has concentrated on description logics that either allow for number restrictions or for existential (...) restrictions. Many applications, however, require to combine these constructors. In this work, we present an algorithm for computing the lcs in the description logic ALEN which comprises both constructors—number and existential restrictions—as well as concept conjunction, primitive negation, and value restrictions. To prove correctness of our lcs algorithm, we develop a structural characterization of subsumption in ALEN. (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.

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)

This chapter contains sections titled: Introduction The ACL2 System A Modeling Problem Case Studies.

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)

The aim of this paper is to clarify the truth-functional interpretation of the logical connective of the material implication. The importance of such clarification lies in the fact that it allows avoiding the supposed paradoxes introduced by C. I. Lewis (1918). I argue that an adequate understanding of the history and purposes of logic is enough to dissolve them away. The defense is based on an exposition of propositional compositionalism. To compare, I also present Stalnaker’s (1968) alternative that seeks (...) to explain the implicit concept of conditionality of conditionals assertions. In order to reinforce my aim I expound the twelve different meanings of ‘implication’ stated by Corcoran (1993) in order to hold that a proper understanding of these meanings allows us to avoid ambiguities and confusions. Finally, I expect to show that despite the possible alternatives, compositionalism is still the best explanation for the truth-functionality account of logical connectives. (shrink)