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 Joint International Conference on Logic Programming, sponsored by the Association for Logic Programming, is a major forum for presentations of research, applications, and implementations in this important area of computer science. Logic programming is one of the most promising steps toward declarative programming and forms the theoretical basis of the programming language Prolog and its various extensions. Logic programming is also fundamental to work in artificial intelligence, where it has been used for nonmonotonic and commonsense (...) reasoning, expert systems implementation, deductive databases, and applications such as computer-aided manufacturing. Krzysztof R. Apt is project leader at the Centre for Mathematics and Computer Science in Amsterdam and part-time Professor in Computer Science at the University of Amsterdam. Topics covered: Theory Foundations. Programming Languages. Implementation. Programming Methodologies and Tools. Applications. Deductive Databases. Artificial Intelligence. Parallelism. (shrink)

This paper is an original attempt to understand the foundations of economic reasoning. It endeavors to rigorously define the relationship between subjective interpretations and objective valuations of such interpretations in the context of theoretical economics. This analysis is substantially expanded through a dynamic approach, where the truth of a valuation results in an updated interpretation or changes in the agent's subjective belief regarding the effectiveness of the selected action as well as the objective reality of the effectiveness of all other (...) possible actions (i.e. consequence realization). Complications arise when the economic agent is presented with a set of actions that render ambiguous preference, or when the effectiveness of an action cannot be perceived upon its selection, thereby necessitating a different theory of choice and consequence realization. (shrink)

. In this paper, the significance of using general logic-systems and finite consequence operators defined on non-organized languages is discussed. Results are established that show how properties of finite consequence operators are independent from language organization and that, in some cases, they depend only upon one simple language characteristic. For example, it is shown that there are infinitely many finite consequence operators defined on any non-organized infinite language L that cannot be generated from any finite logic-system. On (...) the other hand, it is shown that for any nonempty language L, a set map is a finite consequence operator if and only if it is defined by a general logic-system. Simple logic-system examples that determine specific consequence operator properties are given. (shrink)

이 글은 묵자의 철학 가운데 소통문제에 대한 연구이다. 먼저 묵자의 소통을 위한 논증적 이론체계의 구축과정을 살펴보고, 그 논증을 통하여 도출된 이론들을 실천에 옮기는 소통에 집중하고자 하였다. 묵자는 천의지에 의한 의를 소통적 본질로 하여 의존 관계인 사와 실을 소통 방법의 기능으로 삼아 백성들의 삶을 안정시키는 것에 중점을 둔다. 그리고 소통을 형성하는 관계적 언어를 다스림인 치에 두면서, 그 다스림을 내외적 다스림의 논증적 사유체계로 확장시켜 나간다. 이것은 인간이 사물과 접촉함으로써 발현되는 앎(知)으로 나타나 실용적 가치인 이(利)를 창출하는 것이다. 묵자의 소통을 위한 논리는 실리주의를 기초로 (...) 하여 경험적이며, 결과적 사유방식을 체계적으로 이론화 했다. 소통의 핵심인 의는 백성들의 기본적 욕구를 저해하는 삼환을 해결하여 교상리로 귀착 시킨다. 특히 묵자는 인식론을 실의 물드림으로 비유하고, 인간의 이기적 사유를 소통의 이론체계(義-事-實-治-利-染)로 물들게 하여 안생생의 사회, 즉 겸애와 교상리의 이론으로 전쟁을 방비하여 백성들의 안정된 삶과 평화를 펼치는 것을 목적으로 한다. (shrink)

This paper aims at clarifying the nature of Frege's system of logic, as presented in the first volume of the Grundgesetze. We undertake a rational reconstruction of this system, by distinguishing its propositional and predicate fragments. This allows us to emphasise the differences and similarities between this system and a modern system of classical second-order logic.

The main objective o f this descriptive paper is to present the general notion of translation between logical systems as studied by the GTAL research group, as well as its main results, questions, problems and indagations. Logical systems here are defined in the most general sense, as sets endowed with consequence relations; translations between logical systems are characterized as maps which preserve consequence relations (that is, as continuous functions between those sets). In this sense, logics together with translations form a (...) bicomplete category of which topological spaces with topological continuous functions constitute a full subcategory. We also describe other uses of translations in providing new semantics for non-classical logics and in investigating duality between them. An important subclass of translations, the conservative translations, which strongly preserve consequence relations, is introduced and studied. Some specific new examples of translations involving modal logics, many-valued logics, para- consistent logics, intuitionistic and classical logics are also described. (shrink)

This superb collection of papers focuses on a fundamental question in logic and computation: What is a logical system? With contributions from leading researchers--including Ian Hacking, Robert Kowalski, Jim Lambek, Neil Tennent, Arnon Avron, L. Farinas del Cerro, Kosta Dosen, and Solomon Feferman--the book presents a wide range of views on how to answer such a question, reflecting current, mainstream approaches to logic and its applications. Written to appeal to a diverse audience of readers, What is a (...) Logical System? will excite discussion among students, teachers, and researchers in mathematics, logic, computer science, philosophy, and linguistics. (shrink)

Doubts concerning the validity of logic are as old as the empirical criticism of science. In the last two decades the idea that truth is relative to given sets of basic assumptions has been prominent; and the controversy about the principle of excluded middle has focussed renewed attention upon the nature of logic and its fundamental principles.Recent investigations in formal logic have contributed greatly to the understanding of the principles of logic. It is simply a misunderstanding (...) to conclude from them that the logical principles have been suspended, despite the various formal structures which are called “logics.” The purely formal treatment of problems concerning the foundations of logic, while necessarily undertaken as far as it can go, has essential limitations. (shrink)

This paper investigates modular combinations of temporal logic systems. Four combination methods are described and studied with respect to the transfer of logical properties from the component one-dimensional temporal logics to the resulting combined two-dimensional temporal logic. Three basic logical properties are analyzed, namely soundness, completeness, and decidability. Each combination method comprises three submethods that combine the languages, the inference systems, and the semantics of two one-dimensional temporal logic systems, generating families of two-dimensional temporal languages with varying (...) expressivity and varying degrees of transfer of logical properties. The temporalization method and the independent combination method are shown to transfer all three basic logical properties. The method of full join of logic systems generates a considerably more expressive language but fails to transfer completeness and decidability in several cases. So a weaker method of restricted join is proposed and shown to transfer all three basic logical properties. (shrink)

Josiah Royce (1855?1916) was, in addition to being the pre-eminent metaphysician at the turn of the 19th century in the USA, regarded as ?a logician of the first rank?. At the time of his death in 1916, he had begun a substantial and potentially revolutionary project in logic in which he sought to show the connection between logic and ethics, aesthetics, and metaphysics. His system was developed in light of the work of Bertrand Russell and A. B. (...) Kempe and aimed to include Russell's logic as a subsystem. This more comprehensive logic, which Royce called system Σ, brought together an analysis of the character of experience and knowledge with the principles which served to organize interests and direct actions. The result was to be a logical theory framed by ?a profoundly ethical motive as well as a genuinely intellectual one? that would serve as ?a theory of the way in which activities must go on if they go on at all?. This paper examines three stages in the development of Royce's logical system, its relation to the logic of Principia Mathematica, and prospects for its further development. (shrink)

This book addresses the hasty development of modern logic, especially its introducing and embracing various kinds of artificial languages and moving from the study of natural languages to that of artificial ones. This shift seemed extremely helpful and managed to elevate logic to a new level of rigor and clarity. However, the change that logic underwent in this way was in no way insignificant, and it is also far from an insignificant matter to determine to what extent (...) the "new logic" only engaged new and more powerful instruments to answer the questions posed by the "old" one, and to what extent it replaced these questions with new ones. Hence, this movement has generated brand new kinds of philosophical problems that have still not been dealt with systematically. Philosophy of Logical Systems addresses these new kinds of philosophical problems that are intertwined with the development of modern logic. Jaroslav Peregrin analyzes the rationale behind the introduction of the artificial languages of logic; classifies the various tools which were adopted to build such languages; gives an overview of the various kinds of languages introduced in the course of modern logic and the motifs of their employment; discusses what can actually be achieved by relocating the problems of logic from natural language into them; and reaches certain conclusions with respect to the possibilities and limitations of this "formal turn" of logic. This book is both an important scholarly contribution to the philosophy of logic and a systematic survey of the standard logical systems that were established during the short history of modern logic. (shrink)

This book is focused on the first three parts of Bolzano's Theory of Science and introduces a more systematic reconsideration of Bolzano's logical thought. In undertaking this task, the book is intended as an exploration, not so much of the more specifically discursive aspects of Bolzano's logical thought - already amply studied - as much as on identifying the singularly coherent and systematic nature of the logic presented in Bolzano's work.

Fusion is a well-known form of combining normal modal logics endowed with a Hilbert calculi and a Kripke semantics. Herein, fusion is studied over logic systems using sequent calculi labelled with truth values and with a semantics based on a two-sorted algebra allowing, in particular, the representation of general Kripke structures. A wide variety of logics, including non-classical logics like, for instance, modal logics and intuitionistic logic can be presented by logic systems of this kind. A categorical (...) approach of fusion is defined in the context of these logic systems. Preservation of soundness and completeness by fusion is studied. Soundness is preserved without further requirements, completeness is preserved under mild assumptions. (shrink)

Stanislaw Lesniewski’s interests were, for the most part, more philosophical than mathematical. Prior to taking his doctorate at Jan Kazimierz University in Lvov, Lesniewski had spent time at several continental universities, apparently becoming relatively attached to the philosophy of one of his teachers, Hans Comelius, to the chapters of John Stuart Mill’s System of Logic that dealt specifically with semantics, and, in general, to studies of general grammar and philosophy of language. In these several early interests are already (...) to be found the roots of the work that was to occupy Lesniewski’s life: a search for a definitive doctrine of what sorts of things there are in the world, or better, of what language must be like if it is adequately and efficiently to represent the world. (shrink)

This two-volume work, first published in 1843, was John Stuart Mill's first major book. It reinvented the modern study of logic and laid the foundations for his later work in the areas of political economy, women's rights and representative government. In clear, systematic prose, Mill disentangles syllogistic logic from its origins in Aristotle and scholasticism and grounds it instead in processes of inductive reasoning. An important attempt at integrating empiricism within a more general theory of human knowledge, the (...) work constitutes essential reading for anyone seeking a full understanding of Mill's thought. Continuing the discussion of induction, Volume 2 concludes with Book VI, 'On the Logic of the Moral Sciences', in which Mill applies empirical reasoning to human behaviour. A crucial early formulation of his thinking regarding free will and necessity, this book establishes the centrality of 'the social science' to Mill's philosophy. (shrink)

This thorough investigation of the implications, both logical and philosophical, of Lesniewski's systems should do much to arouse interest in this neglected Polish philosopher. The author takes great pains to relate Lesniewski's ideas to those prevailing today in "orthodox" circles of logicians. There is an excellent bibliography.—A. E. F.

Logical works of this period, beginning with Generales Inquisitiones and ending wi th the two dated pieces of 1 Aug. 1690 and 2 Aug. 1690 , are read as a sustained effort, finally successful, to develop a set of axioms and an appropriate schema for the expression of categorical propositions faithful to traditional syllogistic. This same set of axioms is shown to be comprehensive of the propositional calculus of Principia Mathematica, providing that ‘Some A is A’ is not a thesis (...) in an unrestricted sense. There is no indication in the works of this period that Leibniz understood just how significant is this logicalsystem he developed. But it is undeniable that he held tenaciously to this particular set of axioms throughout the period, a set of axioms of great power. (shrink)

As part of our small contribution in dialogue toward better peace development and reconciliation studies, and following Toffler & Toffler’s War and Antiwar (1993), the present article delves into a realm of logic beyond the traditional confines of negation and the excluded middle principle, exploring the nuances of "Otherness" that transcend classical and Nagatomo logics. Departing from the foundational premises of classical Aristotelian logic systems, this exploration ventures into alternative realms of reasoning, specifically examining Neutrosophic Logic and (...) Klein bottle logic (cf. Smarandache, 2005). The study challenges conventional boundaries and explores the implications of embracing paradoxes and self-reference in logic systems, aiming to redefine approaches to understanding truth and reasoning. The paper investigates how these alternative logics open avenues for philosophical inquiry, redefining entropy, and potentially influencing innovative perspectives in free energy systems. Through this exploration, it seeks to expand the discourse on logic, welcoming a broader spectrum of thought beyond established frameworks; and we also discuss shortly a number of possible implementations including in risk management and also Klein bottle entropy redefinition (Tang et al, 2018). (shrink)

Nervous systems are intricately organized on many levels of analysis.The intricate organization invites the development of mathematicalsystems that reflect its logical structure. Particular logical structures and choices of invariants within those structures narrowthe ranges of perceptions that are possible and sensorimotorcoordination that may be selected. As in quantum logic, choicesaffect outcomes.Some of the mathematical tools in use in quantum logic havealready also been used in neurobiology, including the mathematicsof ordered structures and a product like a tensor product. Astheoretical (...) neurobiology is developed on its own foundation, wemay expect a rich dialogue between theoretical neurobiology andquantum logic. (shrink)

We introduce a methodology whereby an arbitrary logic system L can be enriched with temporal features to create a new system T(L). The new system is constructed by combining L with a pure propositional temporal logic T (such as linear temporal logic with “Since” and “Until”) in a special way. We refer to this method as “adding a temporal dimension to L” or just “temporalising L”. We show that the logic system T(L) (...) preserves several properties of the original temporal logic like soundness, completeness, decidability, conservativeness and separation over linear flows of time. We then focus on the temporalisation of first-order logic, and a comparison is make with other first-order approaches to the handling of time. (shrink)

We introduce a methodology whereby an arbitrary logic system L can be enriched with temporal features to create a new system T(L). The new system is constructed by combining L with a pure propositional temporal logic T (such as linear temporal logic with Since and Until) in a special way. We refer to this method as adding a temporal dimension to L or just temporalising L. We show that the logic system T(L) (...) preserves several properties of the original temporal logic like soundness, completeness, decidability, conservativeness and separation over linear flows of time. We then focus on the temporalisation of first-order logic, and a comparison is make with other first-order approaches to the handling of time. (shrink)

"Lesniewski defined ontology, one of his three foundational systems, as 'a certain kind of modernized 'traditional logic' [On the foundations of mathematics (FM), p. 176]. In this respect it is worth bearing in mind that in the 1937-38 academic year Lesniewski taught a course called "Traditional 'formal logic' and traditional 'set theory' on the ground of ontology"; cf. Srzednicki and Stachniak, S. Lesniewski's Systems. Protothetic, 1988, p. 180. On this see Kotarbinski Gnosiology. The scientific approach to the theory (...) of knowledge, 1966, pp. 253-54 [the Polish original was published in 1929], which Lesniewski praised in [FM]: see in particular pp. 373 ff. Kotarbinski noted that Lesniewski "calls his system 'ontology' in harmony with certain terms used earlier (as in.. (shrink)

A foundational text in modern empiricist method, published in 1843 by Victorian England's foremost philosopher of political and social life.

Bernard Bolzano was born in Prague in 1781 and died in 1848 in the same city1. His major work Wissenschaftslehre was published in 1837 in Sulzbach, Germany.Since the publication of Jan Berg’s Bolza...