Modal logic by patrick blackburn cambridge university press. For example, the statement john is happy might be qualified by saying that john is usually happy, in which. Modal logic is a type of formal logic primarily developed in the 1960s that extends classical propositional and predicate logic to include operators expressing modality. Find, read and cite all the research you need on researchgate. Towards a duality result in coalgebraic modal logic.
The development is mathematical prior acquaintance with firstorder logic and its semantics is assumed. An introduction to modal logic 2009 formosan summer school on logic, language, and computation 29 june10 july, 2009. Their combined citations are counted only for the first article. The polytheistic approach to modal logics alethic modal logic. A semantical analysis of secondorder propositional modal logic. The book is for novices and for more experienced readers, with two distinct tracks clearly signposted at the start of each chapter. In addition, the following books and survey articles are recommended the relevant excerpts will be made available in class. We investigate uniform interpolants in propositional modal logics from the prooftheoretical point of view. Rooted models in modal logic mathematics stack exchange. Using wordnet to measure semantic orientations of adjectives. Whether youve loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them.
The authors focus on the use of modal languages as tools to analyze the properties. Technical report 7807, department of mathematics, university of amsterdam, 1978. It was first conceived for modal logics, and later adapted to intuitionistic logic and other nonclassical systems. Aug 22, 2002 modal logic volume 53 of cambridge tracts in theoretical computer science. Modern origins of modal logic stanford encyclopedia of. Thus modal logic can be viewed as a fragment of classical logic, and in contemporary work in modal logic it is commonplace to view it in this way. There are excellent introductions to modal logic today, of which p. Neighborhood semantics for modal logic an introduction. Contingent features would include, for example, the specific number of worlds under consideration, the specific valuation of the atoms, and the choice of an actual world. This paper forms a step in the development of the recently emerged connection between coalgebra and modal logic. A semantical analysis of secondorder propositional modal. The purpose of this paper is to show that such an axiom is indispensable.
It is a very good reference to have if you intend to pursue research in logic. The term modal logic refers to an enrichment of standard formal logic where the standard operations and, or, not, implication and perhaps forall, etc. For example, it will be useful to be familiar with. These notes are meant to present the basic facts about modal logic and so to provide a common. Blackburn, van benthem, and wolter 2007 has become one of the most popular formal frameworks in arti.
Majority logic eric pacuit and samer salame department of computer science. Venema, cambridge university press, cambridge, 2001. Cambridge core programming languages and applied logic modal logic by patrick blackburn. Cambridge university press, cambridge, new york, etc. This very extensive volume represents the current statofa airs in modal logic.
Isbn 9780792353355 isbn 9789401152921 ebook this is a thorough treatment of firstorder modal logic. Weakly aggregative modal logic \\textsf waml\ is a collection of disguised polyadic modal logics with nary modalities whose arguments are all the same. Modal logic,volume 53 of cambridge tracts in theoretical computer science. An advanced, but very accessible, textbook focusing on the main technical results in the area. The choice is between goldblatt 2, hughes and cresswell 3 and chagrov and zakharyaschev 1. An introduction to modal logic 2009 formosan summer school on logic, language, and computation. Algebraic tools for modal logic mai gehrke yde venema esslli01 august 17, 2001 helsinki, finland. Modal logic cambridge tracts in theoretical computer science. At the core of the semantics of modal logic lies the no. Yet, the variety of textbooks available for the wouldbe student is not as rich as in.
Kripke semantics also known as relational semantics or frame semantics, and often confused with possible world semantics is a formal semantics for nonclassical logic systems created in the late 1950s and early 1960s by saul kripke and andre joyal. Sorry, we are unable to provide the full text but you may find it at the following locations. The focus here is on rstorder modal logic as opposed to propositional modal logic which is the focus of most of the. Modal logic can be viewed broadly as the logic of different sorts of modalities, or modes of truth. Independence of the dual axiom in modal k with primitive. Cambridge university press 9780521527149 modal logic. Other readers will always be interested in your opinion of the books youve read. February 2, 2010 x modal logic for open minds there are excellent introductions to modal logic today, of which p.
Cambridge tracts in theoretical computer science, no. The idea is to select a few papers that make use of modal logic you may. A modala word that expresses a modalityqualifies a statement. Our approach is adopted from pitts proof of uniform interpolationin intuitionistic propositional logic 15. Algebraic tools for modal logic mai gehrke yde venema esslli01 august 17, 2001. Epistemic logic stanford encyclopedia of philosophy. Covers core concepts and basic metatheory of propositional modal logic, including rela. For example, the statement john is happy might be qualified by saying that john is usually happy, in which case the term usually is functioning as a modal.
Modal logic volume 53 of cambridge tracts in theoretical computer science. And indeed, the basic modal language over prop can be translated into a. The method is based on a simulation of certain quantifiers ranging over propositional variables and uses a terminating sequent calculus for which structural rules are. Venema, 2000, modal logic,cambridge university press, cambridge, will often be cited in this book. Modal logic cambridge tracts in theoretical computer. Browse other questions tagged logic graphtheory firstorderlogic modeltheory or ask your own question. Browse other questions tagged logic graphtheory firstorder logic modeltheory or ask your own question. For very precise introduction to basic multimodal logic. Researchers in areas ranging from economics to computational linguistics have since realised its worth. Handbook of modal logic edited by johan van benthem, patrick blackburn and frank wolter. In axiomatizing these logics, they resort to an axiom that is not needed when is the modal primitive. Cambridge tracts in theoretical computer science, 29, 2001.
Venema modal logic cambridge tracts in theoretical computer science, 53 cambridge. This suggests that modal and classical logic must be systematically related. Uniform interpolation and propositional quantifiers in. The book covers such issues as quantification, equality including a treatment of frege s morning star evening star puzzle, the notion of existence, nonrigid. Extending modal logic illc universiteit van amsterdam.
This is an excerpt from the recen tly published textb o ok mo dal l o gic b y same. This book has been quite standard in the modal logic community since its publication. First order modal logic by melvin fitting and elliot mehdelsohn. Blog a message to our employees, community, and customers on covid19. On the degree of incompleteness in modal logic and the covering relations in the lattice of modal logics. If modal logic and classical logic are so closely linked, why bother with modal logic at all. It introduces backandforth transformations between coalgebras of simple polynomial functors and certain boolean algebras with operators baos. This is an advanced 2001 textbook on modal logic, a field which caught the attention of computer scientists in the late 1970s.