It is demonstrated that Hamblin's 15 tense theorem does not only hold for temporal logic with linear time but also for branching time. Furthermore three other theorems with finitely many tenses are shown.

This paper specifies classes of framesmaximally omnitemporally characteristic for Thomas' normal modal logicT 2 + and for each logic in the ascending chain of Segerberg logics investigated by Segerberg and Hughes and Cresswell. It is shown that distinct a,scending chains of generalized Segerberg logics can be constructed from eachT n + logic (n 2). The set containing allT n + and Segerberg logics can be totally- (linearly-) ordered but not well-ordered by the inclusion relation. The order type of this ordered (...) set is *( + 1). Throughout the paper my approach is fundamentally semantical. (shrink)

Arguably, there is no substantial, general answer to the question of what makes for the approximate truth of theories. But in one class of cases, the issue seems simply resolved. A wide class of applied dynamical theories can be treated as two-component theories—one component specifying a certain kind of abstract geometrical structure, the other giving empirical application to this structure by claiming that it replicates, subject to arbitrary scaling for units etc., the geometric structure to be found in some real-world (...) dynamical phenomenon. In such a case, a theory is approximately true just if the one geometric structure approximately replicates the other (and if problems remain here, they are problems in geometry, of specifying suitable metric approximation relations, not conceptual problems). This article amplifies and defends this simple approach to approximate truth for dynamical theories. (shrink)

The epsilon calculus improves upon the predicate calculus by systematically providing complete individual terms. Recent research has shown that epsilon terms are therefore the “logically proper names” Russell was not able to formalize, but their use improves upon Russell’s theory of descriptions not just in that way. This paper details relevant formal aspects of the epsilon calculus before tracing its extensive application not just to the theory of descriptions, but also to more general problems with anaphoric reference. It ends by (...) contrasting a Meinongian account of cross-reference in intensional constructions with the epsilon account. (shrink)

This approach does not define a probability measure by syntactical structures. It reveals a link between modal logic and mathematical probability theory. This is shown (1) by adding an operator (and two further connectives and constants) to a system of lower predicate calculus and (2) regarding the models of that extended system. These models are models of the modal system S₅ (without the Barcan formula), where a usual probability measure is defined on their set of possible worlds. Mathematical probability models (...) can be seen as models of S₅. (shrink)

In various arguments, Descartes relies on the principles that conceivability implies possibility and that inconceivability implies impossibility. Those principles are in tension with another Cartesian view about the source of modality, i.e. the doctrine of the free creation of eternal truths. In this paper, I develop a ‘two-modality’ interpretation of the doctrine of eternal truths which resolves the tension and I discuss how the resulting modal epistemology can still be relevant for the contemporary discussion.

In this paper, I will develop a set of boulesic-doxastic tableau systems and prove that they are sound and complete. Boulesic-doxastic logic consists of two main parts: a boulesic part and a doxastic part. By ‘boulesic logic’ I mean ‘the logic of the will’, and by ‘doxastic logic’ I mean ‘the logic of belief’. The first part deals with ‘boulesic’ concepts, expressions, sentences, arguments and theorems. I will concentrate on two types of boulesic expression: ‘individual x wants it to be (...) the case that’ and ‘individual x accepts that it is the case that’. The second part deals with ‘doxastic’ concepts, expressions, sentences, arguments and theorems. I will concentrate on two types of doxastic expression: ‘individual x believes that’ and ‘it is imaginable to individual x that’. Boulesic-doxastic logic investigates how these concepts are related to each other. Boulesic logic is a new kind of logic. Doxastic logic has been around for a while, but the approach to this branch of logic in this paper is new. Each system is combined with modal logic with two kinds of modal operators for historical and absolute necessity and predicate logic with necessary identity and ‘possibilist’ quantifiers. I use a kind of possible world semantics to describe the systems semantically. I also sketch out how our basic language can be extended with propositional quantifiers. All the systems developed in this paper are new. (shrink)

In this paper, I develop a new set of doxastic logical systems and I show how they can be used to solve several well-known problems in doxastic logic, for example the so-called problem of logical omniscience. According to this puzzle, the notions of knowledge and belief that are used in ordinary epistemic and doxastic symbolic systems are too idealised. Hence, those systems cannot be used to model ordinary human or human-like agents' beliefs. At best, they can describe idealised individuals. The (...) systems in this paper can be used to symbolise not only the doxastic states of perfectly rational individuals, but also the beliefs of finite humans. Proof-theoretically, I will use a tableau technique. Every system is combined with predicate logic with necessary identity and ‘possibilist’ quantifiers and modal logic with two kinds of modal operators for relative and absolute necessity. The semantics is a possible world semantics. Finally, I prove that every tableau system in the paper is sound and complete with respect to its semantics. (shrink)

Many people hold that there is a distinctive notion of metaphysical necessity. In this paper I explain why I am skeptical about the view. I examine the sorts of considerations that are adduced for it, and argue that they meet equal and opposite considerations.

The axiomatic presentation of modal systems and the standard formulations of natural deduction and sequent calculus for modal logic are reviewed, together with the difficulties that emerge with these approaches. Generalizations of standard proof systems are then presented. These include, among others, display calculi, hypersequents, and labelled systems, with the latter surveyed from a closer perspective.

This paper contributes to the principled construction of tableau-based decision procedures for hybrid logic with global, difference, and converse modalities. We also consider reflexive and transitive relations. For converse-free formulas we present a terminating control that does not rely on the usual chain-based blocking scheme. Our tableau systems are based on a new model existence theorem.

In [8] it is proved that all the intermediate logics axiomatizable by formulas in one variable, except four of them, are not strongly complete. We considerably improve this result by showing that all the intermediate logics axiomatizable by formulas in one variable, except eight of them, are not strongly ω-complete. Thus, a definitive classification of such logics with respect to the notions of canonicity, strong completeness, ω-canonicity and strong ω-completeness is given.

We construct an extension P of the standard language of classical propositional logic by adjoining to the alphabet of a new category of logical-pragmatic signs. The well formed formulas of are calledradical formulas (rfs) of P;rfs preceded by theassertion sign constituteelementary assertive formulas of P, which can be connected together by means of thepragmatic connectives N, K, A, C, E, so as to obtain the set of all theassertive formulas (afs). Everyrf of P is endowed with atruth value defined classically, (...) and everyaf is endowed with ajustification value, defined in terms of the intuitive notion of proof and depending on the truth values of its radical subformulas. In this framework, we define the notion ofpragmatic validity in P and yield a list of criteria of pragmatic validity which hold under the assumption that only classical metalinguistic procedures of proof be accepted. We translate the classical propositional calculus (CPC) and the intuitionistic propositional calculus (IPC) into the assertive part of P and show that this translation allows us to interpret Intuitionistic Logic as an axiomatic theory of the constructive proof concept rather than an alternative to Classical Logic. Finally, we show that our framework provides a suitable background for discussing classical problems in the philosophy of logic. (shrink)

This article traces the development of possible worlds semantics through the work of: Wittgenstein, 1913-1921; Feys, 1924; McKinsey, 1945; Carnap, 1945-1947; McKinsey, Tarski and Jónsson, 1947-1952; von Wright, 1951; Becker, 1952; Prior, 1953-1954; Montague, 1955; Meredith and Prior, 1956; Geach, 1960; Smiley, 1955-1957; Kanger, 1957; Hintikka, 1957; Guillaume, 1958; Binkley, 1958; Bayart, 1958-1959; Drake, 1959-1961; Kripke, 1958-1965.

Special issue: "Reflecting on the Legacy of C.I. Lewis: Contemporary and Historical Perspectives on Modal Logic".

For Tarski logics, there are simple criteria that enable one to conclude that two premise sets are equivalent. We shall show that the very same criteria hold for adaptive logics, which is a major advantage in comparison to other approaches to defeasible reasoning forms. A related property of Tarski logics is that the extensions of equivalent premise sets with the same set of formulas are equivalent premise sets. This does not hold for adaptive logics. However a very similar criterion does. (...) We also shall show that every monotonic logic weaker than an adaptive logic is weaker than the lower limit logic of the adaptive logic or identical to it. This highlights the role of the lower limit for settling the adaptive equivalence of extensions of equivalent premise sets. (shrink)