Handbook of Philosophical Logic – serie

The first edition of the "Handbook of Philosophical Logic" (four volumes) was published in the period 1983-1989. The second edition of the handbook is intended to comprise some 18 volumes and should provide up-to-date, authoritative, in-depth coverage of all major topics in philosophical logic and its applications in many fields relating to computer science, language, and argumentation. The volumes will no longer be as topic-oriented as with the first edition because of the way the subject has evolved. However the volumes will follow some natural groupings of chapters. This first volume of the second edition contains major contributions on predicate logic, first- and second-order logic, higher-order logic, algorithms and decision problems, and the mathematics of logic programming.

The first edition of the "Handbook of Philosophical Logic" (four volumes) was published in the period 1983-1989. The second edition of the handbook is intended to comprise some 18 volumes and should provide up-to-date, authoritative, in-depth coverage of all major topics in philosophical logic and its applications in many fields relating to computer science, language, and argumentation. The volumes will no longer be as topic-oriented as with the first edition because of the way the subject has evolved. However the volumes will follow some natural groupings of chapters. This is the second volume of the second edition.

The first edition of the "Handbook of Philosophical Logic" (four volumes) was published in the period 1983-1989. The second edition of the handbook is intended to comprise some 18 volumes and should provide up-to-date, authoritative, in-depth coverage of all major topics in philosophical logic and its applications in many fields relating to computer science, language, and argumentation. The volumes will no longer be as topic-oriented as with the first edition because of the way the subject has evolved. However the volumes will follow some natural groupings of chapters. This first volume of the second edition contains major contributions on predicate logic, first- and second-order logic, higher-order logic, algorithms and decision problems, and the mathematics of logic programming.

This fourth volume of the second edition contains major contributions on Conditional Logic, Dynamic Logic, Logics for Defeasible Argumentation, Preference Logic and Diagrammatic Logic. Audience: Students and researchers whose work or interests involve philosophical logic and its applications.

The increased demand for philosophical logic from computer science and artificial intelligence and computational linguistics has accelerated the development of logic as a philosphical subject directly and indirectly. It has pushed research forward, stimulated by the needs of applications. New logic areas became established and old areas were enriched and expanded This series comprises 18 volumes and aims to provide up-to-date, authoritative, in-depth coverage of all major topics in philosophical logic and its applications in many cutting-edge fields relating to computer science, language, argumentation, etc. This fifth volume contains contributions on intuitionistic logic, free logics and partial logic.

This second edition of the sixth volume of the "Handbook of Philosophical Logic" contains contributions on relevance logic, quantum logics, combinators, proofs and implicational logics and paraconsistent logic. It is aimed specifically at students and researchers whose work or interests involve philosophical logic and its applications.

The seventh volume of the Second Edition contains major contributions on Basic Tense Logic, Advanced Tense Logic, Combinations of Tense and Modality, Philosophical Perspectives on Quantification in Tense and Modal Logic as well as Tense and Time. Audience: Students and researchers whose work or interests involve philosophical logic and its applications.

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.

The ninth volume of the Second Edition contains major contributions on Rewriting Logic as a Logical and Semantic Framework, Logical Frameworks, Proof Theory and Meaning, Goal Directed Deductions, Negations, Completeness and Consistency as well as Logic as General Rationality. Audience: Students and researchers whose work or interests involve philosophical logic and its applications.

It is with great pleasure that we are presenting to the community the second edition of this extraordinary handbook. It has been over 15 years since the publication of the first edition and there have been great changes in the landscape of philosophical logic since then. The first edition has proved invaluable to generations of students and researchers in formal philosophy and language, as weIl as to consumers of logic in many applied areas. The main logic article in the Encyclopaedia Britannica 1999 has described the first edition as 'the best starting point for exploring any of the topics in logic'. We are confident that the second edition will prove to be just as good! The first edition was the second handbook published for the logic commu­ nity. It followed the North Holland one volume Handbook 0/ Mathematical Logic, published in 1977, edited by the late Jon Barwise. The four volume Handbook 0/ Philosophical Logic, published 1983-1989 came at a fortunate temporal junction at the evolution of logic. This was the time when logic was gaining ground in computer science and artificial intelligence circles. These areas were under increasing commercial pressure to provide devices which help and/or replace the human in his daily activity. This pressure required the use of logic in the modelling of human activity and organisa­ tion on the one hand and to provide the theoretical basis for the computer program constructs on the other.

The first edition of the Handbook of Philosophical Logic (four volumes) was published in the period 1983-1989 and has proven to be an invaluable reference work to both students and researchers in formal philosophy, language and logic. The second edition of the Handbook is intended to comprise some 18 volumes and will provide a very up-to-date authoritative, in-depth coverage of all major topics in philosophical logic and its applications in many cutting-edge fields relating to computer science, language, argumentation, etc. The volumes will no longer be as topic-oriented as with the first edition because of the way the subject has evolved over the last 15 years or so. However the volumes will follow some natural groupings of chapters. Audience: Students and researchers whose work or interests involve philosophical logic and its applications.

such questions for centuries (unrestricted by the capabilities of any ha- ware). Theprinciplesgoverningtheinteractionofseveralprocesses, forexample, are abstract an similar to principles governing the cooperation of two large organisation. A detailed rule based e?ective but rigid bureaucracy is very much similar to a complex computer program handling and manipulating data. My guess is that the principles underlying one are very much the same as those underlying the other. Ibelievethedayisnotfarawayinthefuturewhenthecomputerscientist will wake up one morning with the realisation that he is actually a kind of formal philosopher! The projected number of volumes for this Handbook is about 18. The subjecthasevolvedanditsareashavebecomeinterrelatedtosuchanextent that it no longer makes sense to dedicate volumes to topics. However, the volumes do follow some natural groupings of chapters. I would like to thank our authors and readers for their contributions and their commitment in making this Handbook a success. Thanksalso to our publication administrator Mrs J.Spurr for her usual dedication and excellence and to Kluwer Academic Publishers (now Springer) for their continuing support for the Handbook. Dov Gabbay King's College London x PREFACE TO THE SECOND EDITION Logic IT Natural Program Arti?cialin- Logic p- language control spec- telligence gramming processing i?cation, veri?cation, concurrency Temporal Expressive Expressive Planning. Extension of logic power of tense power for re- Time depen- Horn clause operators. currentevents. dent data. with time Temporal Speci?cation Eventcalculus. capability. indices. Sepa- of tempo- Persistence Eventcalculus. ration of past ral control. through time- Temporal logic from future Decision prob- the Frame programming.

such questions for centuries (unrestricted by the capabilities of any ha- ware). Theprinciplesgoverningtheinteractionofseveralprocesses, forexample, are abstract an similar to principles governing the cooperation of two large organisation. A detailed rule based e?ective but rigid bureaucracy is very much similar to a complex computer program handling and manipulating data. My guess is that the principles underlying one are very much the same as those underlying the other. Ibelievethedayisnotfarawayinthefuturewhenthecomputerscientist will wake up one morning with the realisation that he is actually a kind of formal philosopher! The projected number of volumes for this Handbook is about 18. The subjecthasevolvedanditsareashavebecomeinterrelatedtosuchanextent that it no longer makes sense to dedicate volumes to topics. However, the volumes do follow some natural groupingsof chapters. Iwould liketothank our authorsand readersfor their contributionsand their commitment in making this Handbook a success. Thanksalso to our publication administrator Mrs J.Spurr for her usual dedication and excellence and to Kluwer Academic Publishers (now Springer) for their continuing support for the Handbook. Dov Gabbay King's College London 10 Logic IT Natural Program Arti?cial in- Logicp- language control spec- telligence gramming processing i?cation, veri?cation, concurrency Temporal Expressive Expressive Planning. Extension of logic power of tense power for re- Time depen- Horn clause operators. current events. dent data. with time Temporal Speci?cation Eventcalculus. capability. indices. Sepa- of tempo- Persistence Event calculus. ration of past ral control. through time- Temporal logic from future Decision prob- theFrame programming. lems. Model Problem. T- checking. poral query language. temporal transactions.

theywereextensivelydiscussedbyallauthorsina3-dayHandbookmeeting. These are: • a chapter on non-monotonic logic • a chapter on combinatory logic and ?-calculus We felt at the time (1979) that non-monotonic logic was not ready for a chapter yet and that combinatory logic and ?-calculus was too far re- 1 moved. Non-monotonic logic is now a very major area of philosop- cal logic, alongside default logics, labelled deductive systems, ?bring l- ics, multi-dimensional, multimodal and substructural logics. Intensive - examinations of fragments of classical logic have produced fresh insights, including at time decision procedures and equivalence with non-classical systems. Perhaps the most impressive achievement of philosophical logic as arising inthepastdecadehasbeenthee?ectivenegotiationofresearchpartnerships with fallacy theory, informal logic and argumentation theory, attested to by the Amsterdam Conference in Logic and Argumentation in 1995, and the two Bonn Conferences in Practical Reasoning in 1996 and 1997. These subjects are becoming more and more useful in agent theory and intelligent and reactive databases. Finally, ?fteen years after the start of the Handbook project, I would like to take this opportunity to put forward my current views about logic in computer science, computational linguistics and arti?cial intelligence. In the early 1980s the perception of the role of logic in computer science was that of a speci?cation and reasoning tool and that of a basis for possibly neat computer languages. The computer scientist was manipulating data structures and the use of logic was one of his options.

This includes obligations and prohibitions in Talmudic deontic logic, the handling of loops in Talmudic logic, Temporal Talmudic logic, and quantum states and disjunctive attacks in Talmudic logic.

This includes obligations and prohibitions in Talmudic deontic logic, the handling of loops in Talmudic logic, Temporal Talmudic logic, and quantum states and disjunctive attacks in Talmudic logic.

This first volume of the second edition contains major contributions on Predicate Logic, First- and Second-order Logic, Higher-order Logic, Algorithms and Decision Problems, and the Mathematics of Logic Programming. Audience: Students and researchers whose work or interests involve philosophical logic and its applications.

The second volume of the second edition contains major contributions on Systems of Deduction, Alternatives to Standard First-order Semantics, Algebraic Logic, Basic and Advanced Many-valued Logic. Audience: Students and researchers whose work or interests involve philosophical logic and its applications.

The third volume of the second edition contains major contributions on Basic and Advanced Modal Logic, Quantification in Modal Logic and Correspondence Theory. Audience: Students and researchers whose work or interests involve philosophical logic and its applications.

This fourth volume of the second edition contains major contributions on Conditional Logic, Dynamic Logic, Logics for Defeasible Argumentation, Preference Logic and Diagrammatic Logic. Audience: Students and researchers whose work or interests involve philosophical logic and its applications.

The fifth volume of the second edition contains major contributions on Intuitionistic Logic, Free Logics and Partial Logic. Audience: Students and researchers whose work or interests involve philosophical logic and its applications.

The sixth volume of the Handbook of Philosophical Logic, Second Edition contains major contributions on Relevance Logic, Quantum Logics, Combinators, Proofs and Implicational Logics and Paraconsistent Logic. Audience: Students and researchers whose work or interests involve philosophical logic and its applications.

The seventh volume of the Second Edition contains major contributions on Basic Tense Logic, Advanced Tense Logic, Combinations of Tense and Modality, Philosophical Perspectives on Quantification in Tense and Modal Logic as well as Tense and Time. Audience: Students and researchers whose work or interests involve philosophical logic and its applications.

The ninth volume of the Second Edition contains major contributions on Rewriting Logic as a Logical and Semantic Framework, Logical Frameworks, Proof Theory and Meaning, Goal Directed Deductions, Negations, Completeness and Consistency as well as Logic as General Rationality. Audience: Students and researchers whose work or interests involve philosophical logic and its applications.

The first edition of the Handbook of Philosophical Logic (four volumes) was published in the period 1983-1989 and has proven to be an invaluable reference work to both students and researchers in formal philosophy, language and logic. The second edition of the Handbook is intended to comprise some 18 volumes and will provide a very up-to-date authoritative, in-depth coverage of all major topics in philosophical logic and its applications in many cutting-edge fields relating to computer science, language, argumentation, etc. The volumes will no longer be as topic-oriented as with the first edition because of the way the subject has evolved over the last 15 years or so. However the volumes will follow some natural groupings of chapters. Audience: Students and researchers whose work or interests involve philosophical logic and its applications.

The first edition of the Handbook of Philosophical Logic (four volumes) was published in the period 1983-1989 and has proven to be an invaluable reference work to both students and researchers in formal philosophy, language and logic. The second edition of the Handbook is intended to comprise some 18 volumes and will provide a very up-to-date authoritative, in-depth coverage of all major topics in philosophical logic and its applications in many cutting-edge fields relating to computer science, language, argumentation, etc. The volumes will no longer be as topic-oriented as with the first edition because of the way the subject has evolved over the last 15 years or so. However the volumes will follow some natural groupings of chapters.

such questions for centuries (unrestricted by the capabilities of any ha- ware). Theprinciplesgoverningtheinteractionofseveralprocesses, forexample, are abstract an similar to principles governing the cooperation of two large organisation. A detailed rule based e?ective but rigid bureaucracy is very much similar to a complex computer program handling and manipulating data. My guess is that the principles underlying one are very much the same as those underlying the other. Ibelievethedayisnotfarawayinthefuturewhenthecomputerscientist will wake up one morning with the realisation that he is actually a kind of formal philosopher! The projected number of volumes for this Handbook is about 18. The subjecthasevolvedanditsareashavebecomeinterrelatedtosuchanextent that it no longer makes sense to dedicate volumes to topics. However, the volumes do follow some natural groupings of chapters. I would like to thank our authors and readers for their contributions and their commitment in making this Handbook a success. Thanksalso to our publication administrator Mrs J.Spurr for her usual dedication and excellence and to Kluwer Academic Publishers (now Springer) for their continuing support for the Handbook. Dov Gabbay King's College London x PREFACE TO THE SECOND EDITION Logic IT Natural Program Arti?cialin- Logic p- language control spec- telligence gramming processing i?cation, veri?cation, concurrency Temporal Expressive Expressive Planning. Extension of logic power of tense power for re- Time depen- Horn clause operators. currentevents. dent data. with time Temporal Speci?cation Eventcalculus. capability. indices. Sepa- of tempo- Persistence Eventcalculus. ration of past ral control. through time- Temporal logic from future Decision prob- the Frame programming.

such questions for centuries (unrestricted by the capabilities of any ha- ware). Theprinciplesgoverningtheinteractionofseveralprocesses, forexample, are abstract an similar to principles governing the cooperation of two large organisation. A detailed rule based e?ective but rigid bureaucracy is very much similar to a complex computer program handling and manipulating data. My guess is that the principles underlying one are very much the same as those underlying the other. Ibelievethedayisnotfarawayinthefuturewhenthecomputerscientist will wake up one morning with the realisation that he is actually a kind of formal philosopher! The projected number of volumes for this Handbook is about 18. The subjecthasevolvedanditsareashavebecomeinterrelatedtosuchanextent that it no longer makes sense to dedicate volumes to topics. However, the volumes do follow some natural groupingsof chapters. Iwould liketothank our authorsand readersfor their contributionsand their commitment in making this Handbook a success. Thanksalso to our publication administrator Mrs J.Spurr for her usual dedication and excellence and to Kluwer Academic Publishers (now Springer) for their continuing support for the Handbook. Dov Gabbay King's College London 10 Logic IT Natural Program Arti?cial in- Logicp- language control spec- telligence gramming processing i?cation, veri?cation, concurrency Temporal Expressive Expressive Planning. Extension of logic power of tense power for re- Time depen- Horn clause operators. current events. dent data. with time Temporal Speci?cation Eventcalculus. capability. indices. Sepa- of tempo- Persistence Event calculus. ration of past ral control. through time- Temporal logic from future Decision prob- theFrame programming. lems. Model Problem. T- checking. poral query language. temporal transactions.

theywereextensivelydiscussedbyallauthorsina3-dayHandbookmeeting. These are: • a chapter on non-monotonic logic • a chapter on combinatory logic and ?-calculus We felt at the time (1979) that non-monotonic logic was not ready for a chapter yet and that combinatory logic and ?-calculus was too far re- 1 moved. Non-monotonic logic is now a very major area of philosop- cal logic, alongside default logics, labelled deductive systems, ?bring l- ics, multi-dimensional, multimodal and substructural logics. Intensive - examinations of fragments of classical logic have produced fresh insights, including at time decision procedures and equivalence with non-classical systems. Perhaps the most impressive achievement of philosophical logic as arising inthepastdecadehasbeenthee?ectivenegotiationofresearchpartnerships with fallacy theory, informal logic and argumentation theory, attested to by the Amsterdam Conference in Logic and Argumentation in 1995, and the two Bonn Conferences in Practical Reasoning in 1996 and 1997. These subjects are becoming more and more useful in agent theory and intelligent and reactive databases. Finally, ?fteen years after the start of the Handbook project, I would like to take this opportunity to put forward my current views about logic in computer science, computational linguistics and arti?cial intelligence. In the early 1980s the perception of the role of logic in computer science was that of a speci?cation and reasoning tool and that of a basis for possibly neat computer languages. The computer scientist was manipulating data structures and the use of logic was one of his options.