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# Topic: Modal logic

 Springer Online Reference Works The domain of logic in which along with the usual statements modal statements are considered, that is, statements of the type  "it is necessary that …" ,  "it is possible that …" ;, etc. Modal logic was formalized for the first time by C.I. Lewis [1], who constructed five propositional systems of modal logic, given in the literature the notations S1–S5 (their formulations are given below). The majority of systems of modal logic which have been studied are based on classical logic; however, systems based on intuitionistic logic have also been discussed (see, for example, [6]). eom.springer.de /M/m064320.htm   (1205 words)

 Logic - Wikipedia, the free encyclopedia The ambiguity is that "formal logic" is very often used with the alternate meaning of symbolic logic as we have defined it, with informal logic meaning any logical investigation that does not involve symbolic abstraction; it is this sense of 'formal' that is parallel to the received usages coming from "formal languages" or "formal theory". The boldest attempt to apply logic to mathematics was undoubtedly the logicism pioneered by philosopher-logicians such as Gottlob Frege and Bertrand Russell: the idea was that mathematical theories were logical tautologies, and the programme was to show this by means to a reduction of mathematics to logic. Logic cut to the heart of computer science as it emerged as a discipline: Alan Turing's work on the Entscheidungsproblem followed from Kurt GĂ¶del's work on the incompleteness theorems, and the notion of general purpose computer that came from this work was of fundamental importance to the designers of the computer machinery in the 1940s. en.wikipedia.org /wiki/Logic   (0 words)

 MOT - MODAL LOGIC Modal learning theory applies a version of possible world semantics in which a possible world is a pair consisting of evidence stream and a state coordinate. Modal logic including in particular, alethic, tense and epistemic logic has grown into a mature field of research with a wide range of applications in both philosophy, linguistics and computer science. Modal operator theory has at its base rather than as a derivative the idea that whatever epistemic axioms and epistemic systems are possible to validate for some epistemic operator is acutely sensitive to the methodological behavior of the agent involved. www.mot.ruc.dk /modal.htm   (2005 words)

 Modal Logic Modal logics are designed to express possibility, necessity, belief, knowledge, temporal progression and other modalities. Temporal logic plays an important role in the specification, derivation, and verification of programs as programs may be viewed as progressing through a sequence of states, a new state after each event in the system. The propositional modal logics share with classical propositional logic the finite model property; if a collection of formulas is satisfiable, it is satisfiable in a finite graph. cs.wwc.edu /~aabyan/Logic/Modal.html   (0 words)

 Hybrid Logic (Stanford Encyclopedia of Philosophy) A major motivation for hybrid logic is to add further expressive power to ordinary modal logic with the aim of being able to formalize the second kind of statements. A model for hybrid logic is a triple (W, R, V) where W is a non-empty set, R is a binary relation on W, and V is a function that to each pair consisting of an element of W and an ordinary propositional symbol assigns an element of the set {0,1}. The semantics of hybrid tense logic is the semantics of hybrid logic, cf. plato.stanford.edu /entries/logic-hybrid   (3905 words)

 Modal Logic (Stanford Encyclopedia of Philosophy) Modal logic is, strictly speaking, the study of the deductive behavior of the expressions ‘it is necessary that’ and ‘it is possible that’. An understanding of modal logic is particularly valuable in the formal analysis of philosophical argument, where expressions from the modal family are both common and confusing. However, the term ‘modal logic’ is used more broadly to cover a family of logics with similar rules and a variety of different symbols. plato.stanford.edu /entries/logic-modal   (8730 words)

 Peter Suber, "Non-Standard Logics" Logics that include apparatus for signifying when two meanings (as opposed to two wffs, truth-values, sets, predicates, functions) are identical, and that analyzes inferences involving meanings. Logics in which the set of implications determined by a given group of premises does not necessarily grow, and can shrink, when new wffs are added to the set of premises. Logics in which the times at which propositions bear certain truth-values can be indicated, in which the "tense" of the assertion can be indicated, and in which truth-values can be affected by the passage of time. www.earlham.edu /~peters/courses/logsys/nonstbib.htm   (2695 words)

 Teaching Informal Modal Logic in Critical Thinking/Informal Logic Classes I have included a module on informal modal logic in all of the informal logic classes I have taught, and I have found it to be successful in motivating student interest and enriching critical thinking skills. Modal logic is the study of one such kind of possibility and necessity, namely logical possibility and logical necessity. Of course, the primary function of this treatment of modal logic is to enhance the student's understanding of modal claims occurring in ordinary language. www.apa.udel.edu /apa/archive/newsletters/v97n2/teaching/logic.asp   (2454 words)

 AiML: Advances in Modal Logic Modal Logic, originally conceived as the logic of necessity and possibility, has developed into a powerful mathematical discipline that deals with (restricted) description languages for talking about various kinds of relational structures. It is well-known that the impetus for the study of modal logic has shifted in recent years. While the origins of the subject lie in the philosophical analysis of specific modalities - alethic, epistemic, deontic, or temporal - many of its more recent developments stem from the realization that systems of modal logic can often be alternatively viewed as decidable fragments of first-order (or occasionally higher-order) logic enjoying interesting computation-theoretic properties. www.aiml.net   (0 words)

 Modal Logic With the exception of the logical axiom governing definite descriptions, all of the logical axioms of our system are necessary truths (the explanation for this will be given in the tutorial on the logic of definite descriptions). In the usual formulation of modal logic, the Rule of Necessitation is taken as a primitive rule of inference. However, when formulating a modal logic in which one of the logical axioms is not a necessary truth, RN must be restricted. mally.stanford.edu /tutorial/modal.html   (1891 words)

 Modal Logic -- Bibliography 'Semantical Considerations on Modal Logics', Acta Philosoρhica Fennica (1963) Modal and Many-Valued Logics, 83-94. 'Algebraic Semantics for Modal Logics I', JSL 31 (1966), 46-65. 'On the Logic of Negation', Societas Scientiarum Fennica Commentationes Physico-Mathematicae, ΧΧΙΙ, 4, 1959. www.clas.ufl.edu /users/jzeman/modallogic/bibliography.htm   (1932 words)

 The Modal Logic \$100 Challenge Logic provides a rich source of challenges, to determine the relationships between different logics, and between different axiomatizations of the same logic. In modal logics, the lattice of relationships between the Kripke based logics up to S5 is a well known structure. One logic is stronger than the other - the theorems of the first are a strict superset of the theorems of the other. www.cs.miami.edu /~tptp/HHDC   (523 words)

 Modal Logic Unfortunately, all the early attempts at modal predicate calculi had unintuitive theorems (see for instance Kripke 1963a), and, moreover, all of them met with difficulties connected with the failure of Leibniz' law of identity, which we shall try to outline. Actually, in order to get different modal logics (and even then not all of them) one has to be a bit more subtle, and have a binary relation on the set of possible worlds--the alternativeness relation. It is possible to gain the expressive power of modal logic without using modal operators by constructing an ordinary truth-functional logic which describes the multiple-world semantics of modal logic directly. www-formal.stanford.edu /jmc/mcchay69/node22.html   (1380 words)

 Modal epistemic logic   (Site not responding. Last check: ) However, the idealizations made by modal epistemic logic are too strong for any realistic agent: they require that agents be very powerful reasoners who know all logical consequences of what they know, including all logical truths. To save modal logic as logic of knowledge, a new interpretation of epistemic logic has been proposed: the concept of implicit knowledge is invented, and modal epistemic logic is now interpreted as describing this concept. That is, epistemic logic is not taken as describing what an agent actually knows, but only what is implicitly represented in his information state, i.e., what logically follows from his actual knowledge. stinfwww.informatik.uni-leipzig.de /~duc/Thesis/node8.html   (0 words)

 ECSTER Debate Contribution Modal logic broadly conceived is thus a much richer and more versatile research paradigm than just, say, interpreting normal modal operators as philosophically or otherwise interesting modalities. The use of modal logic in AI and its interface with philosophy, as witnessed by the TARK and DEON conferences and their proceedings volumes and, for instance, Fagin et al. Maybe a "deeper" reason for the remarkable stability of modal logic and its present flourishing is the ubiquity of modal notions and the fact that so many phenomena lend themselves to the kind of restricted descriptions provided by modal formalisms. www.ida.liu.se /ext/etai/rac/notes/1998/02/debet.html   (1572 words)

 COMP4412 Modal Logic - Home Page Modal logic is useful in many application areas in CS such as artificial intelligence, computer security, correctness of network protocols, agent technology, and language understanding. An acquaintance with propositional logic (or its equivalent in switching logic in EE) is assumed, and the ability to do mathematical proofs involving induction, contradiction, etc., which feature in standard discrete mathematics courses at the second year (sophomore) level. The Australian Logic Summer School in Dec 2004 is series of lectures held in the Australian National University in Canberra for advanced undergraduates and beginning graduate students who wish to understand logic and/or use it in their work. www.cse.unsw.edu.au /~cs4412   (687 words)

 [No title] Modal logic was originally developed to investigate logic under the modes of necessary and possible truth. A modality is a word that when applied to a statement indicates when, where, how, or under what circumstances the statement may be true. Modal languages have been found to be very useful in reasoning about relational structures that are frequently used in mathematics and computer science as well as other areas. vv.cs.byu.edu /logics   (1683 words)

 Modal Logic : Thomas Alspaugh : UCI First-order logic is primarily concerned with truth and its negation. Modal logic additionally considers the concepts of possibility and necessity. α is a modal logic formula that asserts that α is necessarily true. www.ics.uci.edu /~alspaugh/logic/modalLogic.html   (483 words)

 Modal epistemic logic In order to make epistemic logic possible, idealizations were made concerning the reasoning capacities of the agents, and modal systems were proposed to describe such idealized agents. To save modal logic as logic of knowledge, a new interpretation of epistemic logic has been proposed: the concept of implicit knowledge is invented, and modal epistemic logic is now interpreted as describing this concept. That is, epistemic logic is not taken as describing what an agent actually knows, but only what is implicitly represented in his information state, i.e., what logically follows from his actual knowledge. www.informatik.uni-leipzig.de /~duc/Thesis/node8.html   (415 words)

 Advances in Modal Logic : Tools : Computational Tools In recent years the number of computational tools useful for modal logics, and related logics, has increased significantly, and is continously increasing. Logics Workbench (LWB) - A sequent based theorem prover for a range of propositional logics, including modal logics, temporal logics, intuitionistic logics and nonmonotonic logics. Written for an empirical analysis of decision procedures for modal logic. www.cs.man.ac.uk /~schmidt/tools   (0 words)

 Modal logic Traditional logic is based on extension, in that the truth of the logic is found within the supporting statements. Modal logic are based on intention, in that truth is where you find it, and that the reality of many situations is that it is impossible to determine exact truth. Deontic logic is the specific logic about duty, where necessity is has a moral quality to it. changingminds.org /disciplines/argument/types_reasoning/modal_logic.htm   (266 words)

 Modal Logic - Cambridge University Press Now available in paperback, this is a modern, advanced textbook on modal logic, a field which caught the attention of computer scientists in the late 1970s. The development is mathematical; prior acquaintance with first-order logic and its semantics is assumed, and familiarity with the basic mathematical notions of set theory is required. The authors focus on the use of modal languages as tools to analyze the properties of relational structures, including their algorithmic and algebraic aspects, and applications to issues in logic and computer science such as completeness, computability and complexity are considered. www.cambridge.org /uk/catalogue/catalogue.asp?isbn=0521527147   (354 words)

 Advances in Modal Logic, Volume 2 Modal Logic, originally conceived as the logic of necessity and possibility, has developed into a powerful mathematical and computational discipline. Modal and modal-like languages also provide us with families of restricted description languages for relational and topological structures. Complemented with an editorial introduction covering the roots of modal logic, this book is indispensable for any advanced student and researcher in non-classical logic and its applications. cslipublications.stanford.edu /site/1575862727.html   (209 words)

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