Modal Logic, Autumn 2007 FIrst Steps in Modal Logic

Modal logic is sometimes characterized as the logic of necessity and possibility, of “must be” and “may be”. The aim of this book is to present both semantical and syntactical features of the subject and to illustrate gy detailed analysis of the three most popular modal systems S5,S4 and K. The text presupposes some knowledge of classical logic, although the necessary information is briefly recapitulated. Otherwise the material is self-contained. We concentrate on the logic side of the subject and provide philosophical motivations to show the point of the formal work. Most attention is paid to developments which took place after the first third of the 20-th century. Historical topics are only touched upon. This book partially follows of the composition of Hughess and Cresswell 1968 [12] but simplifies some aspects by use of the semantic notions and related Gentzen-type methods. So our first modal system is S5, which is seen as a reformulation of monadic predicate logic. An axiomatic treatment is postponed to a later section. The systematic use of the Gentzen-type approach via refutation procedures also makes this book a suitable introduction to the proof theory of modal logic. Webester’s Dictionary (1952) explains the meaning of some of our notions reference; check at a new edition in the following way: Mode. (Logic) The form in which a proposition connects the predicate and subject, whether by simple, contingent or necessary assertion; the form of the syllogism, as determined by the quantity and quality of the constituent propositions; mood. Modal. (Logic) Indicating, or pertaining to, some mode or modality; expressing modality. Modality. (Logic) That qualification of propositions according to which they are distinguished as asserting (or denying) the possibility, impossibility, contingency, or necessity of their content. A modal relation or quality; a mode or point of view under which an object presents itself to the mind. We shall see how these notions are made precise in the framework of philosophical logic.