Modal Logic and Its Forms

Philosophia, 1972

in Blackburn, P., van Benthem, J., and Wolter, F., Handbook of Modal Logic, Studies in Logic and Practical Reasoning 3, Elsevier 2006, pp. 1153-1218

Rough Sets, 2002

PART I. PROPOSITIONAL MODAL LOGIC 1. Syntax of non-modal propositional logic 7 2. Semantics of non-modal propositional logic 11 3. Syntax of modal propositional logic 21 4. Preliminary analysis of the notion of strict, logical necessity and possibility 25 5. First semantics for modal propositional logic of logical necessity and possibility 28 6. Logical implication and logical equivalence 46 7. Axiomatic systems of modal propositional logic. The system K. 49 18 The tables and the method of the proof originate in C.I.Lewis and C.H.Langford's Symbolic Logic, 1932.

Logic Journal of The Igpl / Bulletin of The Igpl, 1995

2022

In this paper, we deal with the problem of putting together modal worlds that operate in different logic systems. When evaluating a modal sentence 2φ, we argue that it is not sufficient to inspect the truth of φ in accessed worlds (possibly in different logics). Instead, ways of transferring more subtle semantic information between logical systems must be established. Thus, we will introduce modal structures that accommodate communication between logic systems by fixing a common lattice L where different logics build their semantics. The semantics of each logic being considered in the modal structure is a sublattice of L. In this system, necessity and possibility of a statement should not solely rely on the satisfaction relation in each world and the accessibility relation. The value of a formula 2φ will be defined in terms of a comparison between the values of φ in accessible worlds and the common lattice L. We will investigate natural instances where formulas φ can be said to be n...

Mind, 2009

In philosophical logic necessity is usually conceived as a sentential operator rather than a predicate. An intensional sentential operator does not allow one to express quantified statements such as 'There are necessary a posteriori propositions' or 'All laws of physics are necessary' in first-order logic in a straightforward way, while they are readily formalised if necessity is formalised by a predicate. Replacing the operator conception of necessity by the predicate conception, however, causes various problems and forces one to reject many philosophical accounts involving necessity that are based on the use of operator modal logic. We argue that the expressive power of the predicate account can be restored if a truth predicate is added to the language of first-order modal logic, because the predicate 'is necessary' can then be replaced by 'is necessarily true'. We prove a result showing that this substitution is technically feasible. To this end we provide partial possible-worlds-semantics for the language with a predicate of necessity and perform the reduction of necessities to necessary truths. The technique applies also to many other intensional notions that have been analysed by means of modal operators. * We thank Raf De Clercq, Leon Horsten, Hannes Leitgeb, Tim Williamson and two anonymous referees of Mind for useful comments and suggestions.

Artificial Intelligence in Medicine, 1997

Book reviews Sally Popkorn. First Steps in Modal Logic, Cambridge University Press, Cambridge, 1994, 314 pp., ISBN 052146482, (hardback) f25.00, US$39.95.

Studies in Logic and Practical Reasoning, 2007