In this text, a variety of modal logics at the sentential, first-order, and second-order levels are developed with clarity, precision and philosophical insight.

A textbook on modal logic, intended for readers already acquainted with the elements of formal logic, containing nearly 500 exercises. Brian F. Chellas provides a systematic introduction to the principal ideas and results in contemporary treatments of modality, including theorems on completeness and decidability. Illustrative chapters focus on deontic logic and conditionality. Modality is a rapidly expanding branch of logic, and familiarity with the subject is now regarded as a necessary part of every philosopher's technical equipment. Chellas here offers (...) an up-to-date and reliable guide essential for the student. (shrink)

As McKinsey and Tarski showed, the Stone representation theorem for Boolean algebras extends to algebras with operators to give topological semantics for propositional modal logic, in which the “necessity” operation is modeled by taking the interior of an arbitrary subset of a topological space. In this article, the topological interpretation is extended in a natural way to arbitrary theories of full first-order logic. The resulting system of S4 first-order modal logic is complete with respect to such topological semantics.

A propositional system of modal logic is second-order if it contains quantifiers ∀p and ∃p, which, in the standard interpretation, are construed as ranging over sets of possible worlds (propositions). Most second-order systems of modal logic are highly intractable; for instance, when augmented with propositional quantifiers, K, B, T, K4 and S4 all become effectively equivalent to full second-order logic. An exception is S5, which, being interpretable in monadic second-order logic, is decidable.

No detailed description available for "Moral Competence".

The paper gives a physicist's view on the framework of branching space-time, 385--434). Branching models are constructed from physical state assignments. The models are then employed to give a formal semantics for the modal operators ``possibly'' and ``necessarily'' and for the counterfactual conditional. The resulting formal language can be used to analyze quantum correlation experiments. As an application sketch, Stapp's premises LOC1 and LOC2 from his purported proof of non-locality, 300--304) are analyzed.

The modal logic S4.2 is S4 with the additional axiom ◊□A ⊃ □◊A. In this article, the sequent calculus GS4.2 for this logic is presented, and by imposing an appropriate restriction on the application of the cut-rule, it is shown that, every GS4.2-provable sequent S has a GS4.2-proof such that every formula occurring in it is either a subformula of some formula in S, or the formula □¬□B or ¬□B, where □B occurs in the scope of some occurrence of (...) □ in some formula of S. These are just the K5-subformulas of some formula in S which were introduced by us to show the modied subformula property for the modal logics K5 and K5D : 115–122, 2001). Some corollaries including the interpolation property for S4.2 follow from this. By slightly modifying the proof, the finite model property also follows. (shrink)

We reconstruct as much as we can the part of al-Fārābī's treatment of modal logic that is missing from the surviving pages of his Long Commentary on the Prior Analytics. We use as a basis the quotations from this work in Ibn Sīnā, Ibn Rushd and Maimonides, together with relevant material from al-Fārābī's other writings. We present a case that al-Fārābī's treatment of the dictum de omni had a decisive effect on the development and presentation of Ibn Sīnā's (...) class='Hi'>modal logic. We give further evidence that the Harmonisation of the Opinions of Plato and Aristotle was not written by al-Fārābī. (shrink)

In an English article (‘On Expressions’) Professor Shen Youding writes, ‘the meaning of a name is not the object which is mentioned by means of it’ (Shen 1992: 11). This remark touches on a big issue that has divided contemporary philosophers of language. On the one side is the Millian (after J.S. Mill), who maintains that the semantic value of a name is the object which it designates, denotes, or refers to (as I use them here, these three terms are (...) interchangeable). [1] On the other side is the Fregean (after Gottlob Frege), who thinks that a name has a sense in addition to a reference. [2] Though Professor Sheng’s remark is too brief for us to claim that he would have been prepared to endorse the Fregean idea, it is clear that he was not a Millian. (shrink)

This paper is devoted to the completeness issue of RMLCI — the relative modal logic with composition and intersection— a restriction of the propositional dynamic logic with intersection. The trouble with RMLCI is that the operation of intersection is not modally definable. Using the notion of mosaics, we give a new proof of a theorem considered in a previous paper “Complete axiomatization of a relative modal logic with composition and intersection”. The theorem asserts that the proof theory of (...) RMLCI is complete for the standard Kripke semantics of RMLCI. (shrink)

The aim of this paper is to investigate the problem of existential import in Abelard's modal logic, and to ask whether the system of logical relationships that he proposes for modal propositions ma...

We consider a modal language over crisp frames and formulas evaluated on a finite MTL-chain (a linearly ordered commutative integral residuated lattice). We first show that the basic modal abstract logic with constants for the values of the MTL-chain is the maximal abstract logic satisfying Compactness, the Tarski Union Property and strong invariance for bisimulations. Finally, we improve this result by replacing the Tarski Union Property by a relativization property.