Tense Logic

When added to the usual truth conditions from standard logic, the truth conditions given above for the tense operators provide adequate definitions of truth and falsity for the whole of tense logic. In turn the other semantical concepts ...

Tense Logic

This monograph is designed to provide an introduction to the principal areas of tense logic. Many of the developments in this ever-growing field have been intentionally excluded to fulfill this aim. Length also dictated a choice between the alternative notations of A. N. Prior and Nicholas Rescher - two pioneers of the subject. I choose Prior's because of the syntactical parallels with the language it symbolizes and its close ties with other branches of logi cal theory, especially modal logic. The first chapter presents a wider view of the material than later chapters. Several lines of development are consequently not followed through the remainder of the book, most notably metric systems. Although it is import ant to recognize that the unadorned Prior-symbolism can be enriched in vari ous ways it is an advanced subject as to how to actually carry off these enrichments. Readers desiring more information are referred to the appropri ate literature. Specialists will notice that only the first of several quantifi cational versions of tense logic is proven complete in the final chapter. Again constraints of space are partly to blame. The proof for the 'star' systems is wildly complex and at the time of this writing is not yet ready for publi cation.

Tense and Tense Logic

INTRODUCTION In recent years there has grown up a branch of symbolic logic called tense logic. This logic makes use of a symbolic language which contains, in addition to the symbols of ordinary logic, special symbols called tense ...

Tense and Tense Logic


Temporal Logic

Dov GABBAY: Model Theory for Tense Logics (Jerusalem, 1969; Scientific Report No. 1 of the Applied Logic Branch of the Hebrew University; Multilithed). MASSEY (1969). GERALD J. MASSEY: Tense Logic! Why Bother? Nous, vol. 3 (1969), pp.

Temporal Logic

This book is an introduction to temporal logic, a now flourishing branch of philosophical logic whose origin is of recent date, its main impetus having been provided by the publication in the late 1950s of A. N. PRIOR'S pioneering book, Time and Modality (Oxford, The Clarendon Press, 1957). Virtually all work in the field to around 1966 is surveyed in PRIOR'S elegant treatise Past, Present and Future (Oxford, The Clarendon Press, 1967). In consequence, it is no simple matter to write a comprehensive book on the subject with out merely rehearsing material already dealt with in PRIOR'S works. We believe, however, that the present book succeeds in this difficult endeavor because it approaches established materials from wholly novel points of departure, and is thus able to attain new perspectives and achieve new results. Its introductory character notwithstanding, the present work is consequently in substantial measure devoted to an exposition of new findings and a demonstration of new results. Parts of the book have been published previously. Chapter II is a modified version of an article of the same title by N. RESCHER and JAMES GARSON in The Journal of Symbolic Logic (vol. 33 [1968], pp.537-548). And Chapter XIII is a modified version of the article "Temporally Conditioned Descriptions" by N. RESCHER and JOHN ROBISON in Ratio, vol. 8 (1966), pp. 46-54. The authors are grateful to Professors GARSON and ROBISON, and to the editors of the jounal involved, for their permission to use this materials here.

Investigations in Modal and Tense Logics with Applications to Problems in Philosophy and Linguistics

[9] Fine, K.: 1970, 'Propositional Quantifiers in Modal Logics', Theoria 36, 336–346. [10] Fine, K.: 1970, ... [17] Gabbay, D. M.: 1972, Tense Systems with Discrete Moments of Time', Journal of Philosophical Logic 1, 35–45.

Investigations in Modal and Tense Logics with Applications to Problems in Philosophy and Linguistics

This book is intended to serve as an advanced text and reference work on modal logic, a subject of growing importance which has applications to philosophy and linguistics. Although it is based mainly on research which I carried out during the years 1969-1973, it also includes some related results obtained by other workers in the field (see the refer ences in Part 7). Parts 0, 1 and 2, can be used as the basis of a one year graduate course in modal logic. The material which they contain has been taught in such courses at Stanford since 1970. The remaining parts of the book contain more than enough material for a second course in modal logic. The exercises supplement the text and are usually difficult. I wish to thank Stanford University and Bar-Han University for making it possible for me to continue and finish this work, and A. Ungar for correcting the typescript. Bar-Ilan University, Israel Dov M. GABBA Y PART 0 AN INTRODUCTION TO GENERAL INTENSIONAL LOGICS CHAPTER 0 CONSEQUENCE RELATIONS Motivation We introduce the notions of a consequence relation (which is a generalization of the notion of a logical system) and of a semantics. We show that every consequence relation is complete for a canonical semantics. We define the notion of one semantics being Dian in another and study the basic properties of this notion. The concepts of this chapter are generalizations of the various notions of logical system and possible world semantics found in the literature.

Temporal Logic and State Systems

In fact, there is also a “modal approach” to this topic, called tense logic, which is very close to temporal logic as described here. “Basic” tense logic is an extension of classical propositional logic by unary tense operators for ...

Temporal Logic and State Systems

Temporal logic has developed over the last 30 years into a powerful formal setting for the specification and verification of state-based systems. Based on university lectures given by the authors, this book is a comprehensive, concise, uniform, up-to-date presentation of the theory and applications of linear and branching time temporal logic; TLA (Temporal Logic of Actions); automata theoretical connections; model checking; and related theories. All theoretical details and numerous application examples are elaborated carefully and with full formal rigor, and the book will serve as a basic source and reference for lecturers, graduate students and researchers.

Temporal Logic

But if somebody insists that this category Ac must refer strictly to the past, we could obtain this by a metrical tense-logical form, as in P(n)F(m)q, where n>m. We mentioned earlier three differences between Jespersen and Reichenbach ...

Temporal Logic

Temporal Logic: From Ancient Ideas to Artificial Intelligence deals with the history of temporal logic as well as the crucial systematic questions within the field. The book studies the rich contributions from ancient and medieval philosophy up to the downfall of temporal logic in the Renaissance. The modern rediscovery of the subject, which is especially due to the work of A. N. Prior, is described, leading into a thorough discussion of the use of temporal logic in computer science and the understanding of natural language. Temporal Logic: From Ancient Ideas to Artificial Intelligence thus interweaves linguistic, philosophical and computational aspects into an informative and inspiring whole.

Advances in Temporal Logic

1951, Essays on Logic and Language. Blackwell, Oxford. Hasle, P.: 1997, “The Problem of Predestination - as a prelude to A. N. Prior's tense logic'. To appear in M. Wegener (editor): Time, Creation and World-Order. 22 p.

Advances in Temporal Logic

Time is a fascinating subject and has long since captured mankind's imagination, from the ancients to modern man, both adult and child alike. It has been studied across a wide range of disciplines, from the natural sciences to philosophy and logic. Today, thirty plus years since Prior's work in laying out foundations for temporal logic, and two decades on from Pnueli's seminal work applying of temporal logic in specification and verification of computer programs, temporal logic has a strong and thriving international research community within the broad disciplines of computer science and artificial intelligence. Areas of activity include, but are certainly not restricted to: Pure Temporal Logic, e. g. temporal systems, proof theory, model theory, expressiveness and complexity issues, algebraic properties, application of game theory; Specification and Verification, e. g. of reactive systems, ofreal-time components, of user interaction, of hardware systems, techniques and tools for verification, execution and prototyping methods; Temporal Databases, e. g. temporal representation, temporal query ing, granularity of time, update mechanisms, active temporal data bases, hypothetical reasoning; Temporal Aspects in AI, e. g. modelling temporal phenomena, in terval temporal calculi, temporal nonmonotonicity, interaction of temporal reasoning with action/knowledge/belief logics, temporal planning; Tense and Aspect in Natural Language, e. g. models, ontologies, temporal quantifiers, connectives, prepositions, processing tempo ral statements; Temporal Theorem Proving, e. g. translation methods, clausal and non-clausal resolution, tableaux, automata-theoretic approaches, tools and practical systems.

Temporal Logic of Programs

Weizmann Inst. of Science, Rehovot, Israel, Rep. CS82-12 Ben-Ari, M., Manna, Z., Pnueli, A. (1983): The temporal logic of branching time. Acta Inf. 20, 207-226 Burgess, J. (1982): Axioms for tense logic ...

Temporal Logic of Programs

Introduction to the temporal logic of - in particular paral- lel - programs.Divided into three main parts: - Presenta- tion of the pure temporal logic: language, semantics, and proof theory; - Representation of programs and their proper- ties within the language of temporal logic; - Application of the logical apparatus to the verification of program proper- ties including a new embedding of Hoare's logic into the temporal framework.

On the Logical Analysis of Tense and Aspect

Methodologically, we base our approach on the system ITL of "improved" tense logic first given in Sqvist ... well as gradual becoming in a tense-logical framework; for a fruitful earlier attempt in this direction, see Hoepelman (1974).

On the Logical Analysis of Tense and Aspect

This book is intended for linguistic specialists, and deals with several problematic issues related to the linguistic structure of the English verb within a semantic framework. It contains five papers written within a research project the aim of which was to describe the central categories of the English verb (viz. tense and aspect) by means of methods and descriptive devices generally used in the field of formal logic. The papers discuss areas of the English temporal system that are notoriously difficult to grasp both for learners of the language and grammarians.

The Temporal Logic of Reactive and Concurrent Systems

Another approach and motivation for the study of temporal logic is through the logical analysis of natural languages. It views the development of temporal logic as the formalization of linguistic conventions with regard to tenses into a ...

The Temporal Logic of Reactive and Concurrent Systems

Reactive systems are computing systems which are interactive, such as real-time systems, operating systems, concurrent systems, control systems, etc. They are among the most difficult computing systems to program. Temporal logic is a formal tool/language which yields excellent results in specifying reactive systems. This volume, the first of two, subtitled Specification, has a self-contained introduction to temporal logic and, more important, an introduction to the computational model for reactive programs, developed by Zohar Manna and Amir Pnueli of Stanford University and the Weizmann Institute of Science, Israel, respectively.

Hybrid Logic and its Proof Theory

In tense logic the elements of the set W are called moments or instants and the accesibility relation R is now also called the earlier-later relation. It is straightforward to modify the translations STa and HT in the previous section ...

Hybrid Logic and its Proof Theory

This is the first book-length treatment of hybrid logic and its proof-theory. Hybrid logic is an extension of ordinary modal logic which allows explicit reference to individual points in a model (where the points represent times, possible worlds, states in a computer, or something else). This is useful for many applications, for example when reasoning about time one often wants to formulate a series of statements about what happens at specific times. There is little consensus about proof-theory for ordinary modal logic. Many modal-logical proof systems lack important properties and the relationships between proof systems for different modal logics are often unclear. In the present book we demonstrate that hybrid-logical proof-theory remedies these deficiencies by giving a spectrum of well-behaved proof systems (natural deduction, Gentzen, tableau, and axiom systems) for a spectrum of different hybrid logics (propositional, first-order, intensional first-order, and intuitionistic).

Specifying Message Passing and Time Critical Systems with Temporal Logic

This resulted in an orientation towards the way temporal logic had been studied by philosophers for decades ( in philosophy temporal logic is often called tense logic ) . Investigations of metric temporal logic about the interplay of ...

Specifying Message Passing and Time Critical Systems with Temporal Logic

Free radicals, which are key intermediates in many thermal, photochemical and radiation processes, are important for a proper understanding of fundamental natural processes and the successful development of organic syntheses. After about one decade volume II/18 serves as a supplement and extension to volume II/13 and covers rate constants and other kinetic data of free radical reactions in liquids. Furthermore II/18 contains new chapters on reactions of radicals in excited states and of carbenes, nitrenes and analogues. Selected species in aqueous solutions for which other compilations are available were deliberately omitted as before, and for the same reason electron transfer equilibria of organic radicals were not covered.

Temporal Logic

In particular , if we want to model the notion of change in time in a given application ( such as that in temporal reasoning ) and the dynamic properties of certain problems such as simulation , why not use temporal logic in the first ...

Temporal Logic

This volume constitutes the proceedings of the First International Conference on Temporal Logic (ICTL '94), held at Bonn, Germany in July 1994. Since its conception as a discipline thirty years ago, temporal logic is studied by many researchers of numerous backgrounds; presently it is in a stage of accelerated dynamic growth. This book, as the proceedings of the first international conference particularly dedicated to temporal logic, gives a thorough state-of-the-art report on all aspects of temporal logic research relevant for computer science and AI. It contains 27 technical contributions carefully selected for presentation at ICTL '94 as well as three surveys and position papers.

Papers on Time and Tense

T12 and T13 mean that we could define Uab as Ta ( Fb ) , and if we do so we can replace UT1-4 by the last section's 04 ( Op Gp ) and 05 ( Op Hp ) and the tense logic Kt . Proofs of the UT's from these and a system which will shortly be ...

Papers on Time and Tense

This is a revised and expanded edition of a seminal work in the logic and philosophy of time, originally published in 1968. Arthur N. Prior (1914-1969) was the founding father of temporal logic, and his book offers an excellent introduction to the fundamental questions in the field. Several important papers have been added to the original selection, as well as a comprehensive bibliography of Prior's work and an illuminating interview with his widow, Mary Prior. In addition, the Polish logic which made Prior's writings difficult for many readers has been replaced by standard logical notation. This new edition will secure the classic status of the book.

The Logic of Time

In the next section, specific point structures such as Z or Q will be studied with respect to their tense-logical theories; just as their firstorder theories were determined in Section I.2.1. But besides, there is also the question of ...

The Logic of Time

That philosophical themes could be studied in an exact manner by logical meanS was a delightful discovery to make. Until then, the only outlet for a philosophical interest known to me was the production of poetry or essays. These means of expression remain inconclusive, however, with a tendency towards profuseness. The logical discipline provides so me intellectual backbone, without excluding the literary modes. A master's thesis by Erik Krabbe introduced me to the subject of tense logic. The doctoral dissertation of Paul N eedham awaked me (as so many others) from my dogmatic slumbers concerning the latter's mono poly on the logical study of Time. Finally, a set of lecture notes by Frank Veltman showed me how classical model theory is just as relevant to that study as more exotic intensional techniques. Of the authors whose work inspired me most, I would mention Arthur Prior, for his irresistible blend of logic and philosophy, Krister Segerberg, for his technical opening up of a systematic theory, and Hans Kamp, for his mastery of all these things at once. Many colleagues have made helpful comments on the two previous versions of this text. I would like to thank especially my students Ed Brinksma, Jan van Eyck and Wilfried Meyer-Viol for their logical and cultural criticism. The drawings were contributed by the versatile Bauke Mulder. Finally, Professor H intikka's kind appreciation provided the stimulus to write this book.

Handbook of Philosophical Logic

The question whether an axiomatically presented normal temporal logic A is properly displayable thus reduces to the question whether A can be axiomatized by primitive axioms over Kt . The implicit use of tense logic in the structural ...

Handbook of Philosophical Logic

suchquestionsforcenturies(unrestrictedbythecapabilitiesofanyhard­ ware). Theprinciplesgoverningtheinteractionofseveralprocesses,forexample, areabstractansimilartoprinciplesgoverningthecooperationoftwolarge organisation.Adetailedrulebasedeffectivebutrigidbureaucracyisvery muchsimilartoacomplexcomputerprogramhandlingandmanipulating data. Myguessisthattheprinciplesunderlyingoneareverymuchthe sameasthoseunderlyingtheother. Ibelievethedayisnotfarawayinthefuturewhenthecomputerscientist willwakeuponemorningwiththerealisationthatheisactuallyakindof formalphilosopher! TheprojectednumberofvolumesforthisHandbookisabout18.The subjecthasevolvedanditsareashavebecomeinterrelatedtosuchanextent thatitnolongermakessensetodedicatevolumestotopics.However,the volumesdofollowsomenaturalgroupingsofchapters. Iwouldliketothankourauthorsarereadersfortheircontributionsand theircommitmentinmakingthisHandbookasuccess. Thanksalsoto ourpublicationadministratorMrsJ.Spurrforherusualdedicationand excellenceandtoKluwerAcademicPublishersfortheircontinuingsupport fortheHandbook. DovGabbay King'sCollegeLondon x Logic II IT Natural Program Artificialin­ Logic p- language controlspec­ telligence gramming processing ification, verification, concurrency Temporal Expressive Expressive Planning. Extension of logic poweroftense power for re­ Time depen­ Horn clause operators. currentevents. dent data. with time Temporal Specification Eventcalculus. capability. indices. Sepa­ of tempo- Persistence Eventcalculus. rationofpast ral control. throughtime­ Temporallogic fromfuture Decisionprob­ the Frame programming. Problem.Tem­ lems. Model checking. poral query language. temporal transactions. Modal logic. generalised Actionlogic Beliefrevision. Negation by Multi-modal quantifiers Inferential failure and logics databases modality Algorithmic Discourse rep­ New logics. Generaltheory Proceduralap­ proof resentation. Generic theo­ of reasoning. proachtologic Direct com- remprovers Non-monotonic putation on systems linguisticinput Non­ Resolving Loopchecking. Intrinsiclogical Negation by monotonic ambigui- Non-monotonic discipline for failure.Deduc­ reasoning ties. Machine decisionsabout AI. Evolving tivedatabases translation. loops. Faults and com­ Document insystems. municating classification. databases Relevance theory Probabilistic logicalanalysis Realtimesys­ Expert sys­ Semantics for and fuzzy oflanguage tems tems.Machine logicprograms logic learning Intuitionistic Quantifiers in Constructive Intuitionistic Horn clause logic logic reasoning and logicisabetter logic is really proof theory logical basis intuitionistic.

Tense Reference and Worldmaking

These are the issues on which tense logic and the modeltheoretic semantics on which tense logic is , for the most part , based offer only hand - waving : sentences are “ interpreted ” by being given an “ assignment , ” and they are true ...

Tense  Reference  and Worldmaking

Using Reichenbach's (1947) theory of tenses and temporal structures as a point of departure, McGilvray modifies it to produce a theory of his own. Analysing the difficulties Reichenbach's theory has in explaining the relationship of a speaker to a world, he introduces a new model for this relationship based on the three-interval temporal topology that Reichenbachian theory assigns to the sentences of natural languages. McGilvray explains and defends in detail Reichenbach's theory of tense and temporal structure, criticising and rejecting the major rival theory, found in tense logic. He also applies Reichenbach's nonstandard topology to English, showing that it is correct for the language. A significant aspect of McGilvray's study is the supplementing of Reichenbach's topology by including speakers, sentences, situations, and things spoken about with the temporal intervals. McGilvray relocates and reinterprets a prime source of faulty intuitions concerning time and tense -- our feeling that the past, present, and future must be thought of in terms of the settled, the immediate, and the unsettled. He uses his theory to explain the temporal and semantic structure of complex constructions in English, including propositional attitudes, modals, and conditionals. As well, he adapts the structure that Reichenbach's theory assigns to sentences to the aspects perfective (complete) and imperfective (incomplete). The novel view of temporal and semantic structure developed by McGilvray touches on virtually all the puzzles concerning the philosophy of language -- meaning and meaningfulness, the nature of reference, truth, propositions, and worldmaking. His emphasis is on how the speaker, by articulating sentences and understanding them, is both free and constrained -- free to describe something which can be located at any time and in any world, but constrained by the beliefs, evidence, information, and commitments held or made at the time of speech.

Tense Attitudes and Scope

At this point, I will briefly discuss the formal properties of tense logic (i.e., logical systems that incorporate sentential tense operators, as in (11b)) and “standard logic” (i.e., others that incorporate temporal terms in the ...

Tense  Attitudes  and Scope

Tense, Attitudes, and Scope is a model-theoretic inquiry into the semantics of tense in natural language. The book presents the view that the semantic contribution of tense is made in relation to structurally higher expressions (the `relative tense theory') and argues against the view that tenses are all indexicals. This idea is formally encoded as a de se analysis of attitudes, originally proposed by Lewis, coupled with a sequence-of-tense rule posited for English. An auxiliary proposal is made to account for some exceptional cases (e.g. so-called double-access sentences), which invokes de re attitudes about temporal entities (states or intervals). Since the proposed account assumes that the interpretation of tense is structure-dependent, it also correctly predicts scope interactions between tenses and NPs. Tense, Attitudes, and Scope is intended for scholars and graduate students in formal semantics, syntax-semantics interface, philosophy of language and Japanese linguistics.

Tense Logic

BENNETT , M . : 1973 , ' Two Puzzles Concerning Tense and Aspect in English ' , presented at a symposium on Richard Montague ' s Philosophy of Language , held at a joint meeting of the Association for Symbolic Logic and the Pacific ...

Tense Logic


Facing the Future

On the other hand, the technical devices and conceptual ideas of modal logic due especially to Kripke are essential to both plain or linear tense logic, and to the historical modalities of branching time. 8A.2 Prior's linear tense ...

Facing the Future

Here is an important new theory of human action, a theory that assumes actions are founded on choices made by agents who face an open future. It is a theory that makes indeterminism not only intelligible but illuminating. Tools from philosophy of language and philosophical logic help generate a full-scale account of agents "seeing to it that." The authors then proceed to clarify a variety of action-related topics such as determinism vs. indeterminism, imperatives, promises, strategies, joint agency, "could have done otherwise," deontic constructions, and assertions about a not yet settled future.