Possible Worlds in Use

The paper is a brief survey of the most important semantic constructions founded on the concept of possible world. It is impossible to capture in one short paper the whole variety of the problems connected with manifold applications of possible worlds. Hence, after a brief explanation of some philosophical matters I take a look at possible worlds from rather technical standpoint of logic and focus on the applications in formal semantics. In particular, I would like to focus on the fruitful marriage of possible world semantics and algebra and its evolution leading to very general construction of Wójcicki called referential semantics and some of its refinements. The presentation is informal and sketchy; the main purpose is to put in one place a short, and readable I hope, description of the most important constructions and to point out the main sources of these solutions.

[1]  Steven K. Thomason,et al.  Semantic analysis of tense logics , 1972, Journal of Symbolic Logic.

[2]  Josep Maria Font,et al.  A Survey of Abstract Algebraic Logic , 2003, Stud Logica.

[3]  N. Cocchiarella,et al.  Situations and Attitudes. , 1986 .

[4]  Rudolf Carnap.  Modalities and Quantification , 1946, J. Symb. Log..

[5]  Saul A. Kripke,et al.  Semantical Analysis of Modal Logic I Normal Modal Propositional Calculi , 1963 .

[6]  Bas C. van Fraassen,et al.  Current Issues in Quantum Logic , 1981 .

[7]  B. Jack Copeland,et al.  The Genesis of Possible Worlds Semantics , 2002, J. Philos. Log..

[8]  K. Lambert.  Philosophical Problems in Logic , 1970 .

[9]  S. Babyonyshev.  Fully Fregean Logics , 2003, Reports Math. Log..

[10]  Pseudo-referential Matrix Semantics for Propositional Logics , 2008 .

[11]  Robert Goldblatt,et al.  Mathematical modal logic: A view of its evolution , 2003, J. Appl. Log..

[12]  R. A. Bull,et al.  Basic Modal Logic , 1984 .

[13]  Y. Bar-Hillel.  V.—INDEXICAL EXPRESSIONS , 1954 .

[14]  M. Fitting.  Proof Methods for Modal and Intuitionistic Logics , 1983 .

[15]  Jan Woleński.  Deontic logic and possible worlds semantics: A historical sketch , 1990, Stud Logica.

[16]  R. Goldblatt.  Metamathematics of modal logic , 1974, Bulletin of the Australian Mathematical Society.

[17]  Olivier Roy,et al.  Preference logic, conditionals and solution concepts in games , 2005 .

[18]  J. Czelakowski.  Equivalential logics (II) , 1981 .

[19]  A. Chagrov,et al.  Modal Logic (Oxford Logic Guides, vol. 35) , 1997 .

[20]  Martin Sebastian Gerson.  A comparative study of modal propositional semantics. , 1974 .

[21]  J. Czelakowski.  Partial Referential Matrices for Quantum Logics , 1981 .

[22]  Andrzej Indrzejczak,et al.  LABELLED TABLEAU CALCULI FOR WEAK MODAL LOGICS , 2008 .

[23]  Ryszard Wójcicki.  A Logic is Referential iff it is Selfextensional , 2003, Stud Logica.

[24]  M. de Rijke,et al.  Modal Logic , 2001, Cambridge Tracts in Theoretical Computer Science.

[25]  Alessandra Palmigiano,et al.  Referential semantics: duality and applications , 2006, Reports Math. Log..

[26]  Marek Tokarz.  Synonymy in sentential languages: a pragmatic view , 1988, Stud Logica.

[27]  James W. Garson,et al.  Quantification in Modal Logic , 1984 .

[28]  Richard L. Mendelsohn,et al.  First-Order Modal Logic , 1998 .

[29]  Barry Loewer.  Cotenability and counterfactual logics , 1979, J. Philos. Log..

[30]  David Kaplan,et al.  On the logic of demonstratives , 1979, J. Philos. Log..

[31]  Gary M. Hardegree,et al.  Algebraic Methods in Philosophical Logic , 2001 .

[32]  Richard Spencer-Smith,et al.  Modal Logic , 2007 .

[33]  Ryszard Wójcicki.  Referential Matrix Semantics for Propositional Calculi , 1982 .

[34]  Roman Suszko,et al.  Formalna teoria wartości logicznych I , 1957 .

[35]  Michael Zakharyaschev,et al.  Modal Logic , 1997, Oxford logic guides.

[36]  Ryszard Wójcicki.  R. Suszko's situational semantics , 1984 .

[37]  David Makinson,et al.  A generalisation of the concept of a relational model for modal logic1 , 2008 .

[38]  A. Tarski.  Fundamentale Begriffe der Methodologie der deduktiven Wissenschaften. I , 1930 .

[39]  Grzegorz Malinowski,et al.  Referentiality and Matrix Semantics , 2011, Stud Logica.

[40]  Dana S. Scott,et al.  Advice on Modal Logic , 1970 .

[41]  Saul Kripke,et al.  A completeness theorem in modal logic , 1959, Journal of Symbolic Logic.

[42]  Grzegorz Malinowski,et al.  Many-Valued Logics , 1994 .

[43]  Ryszard Wójcicki,et al.  Theory of Logical Calculi , 1988 .

[44]  E. J. Lemmon,et al.  Algebraic semantics for modal logics I , 1966, Journal of Symbolic Logic (JSL).

[45]  J. Łoś,et al.  Remarks on sentential logics , 1958 .

[46]  David Lewis.  Counterpart Theory and Quantified Modal Logic , 1968 .

[47]  A. Tarski,et al.  The Algebra of Topology , 1944 .