In this paper we present a new modeling for belief revision that is what we term irrevocable. This modeling is of philosophical interest since it captures some features of suppositional reasoning, and of formal interest since it is closely connected with AGM, yet provides for iterated belief revision. The analysis is couched in terms of dynamic doxastic logic.

Modal Logic, originally conceived as the logic of necessity and possibility, has developed into a powerful mathematical and computational discipline. It is the main source of formal languages aimed at analyzing complex notions such as common knowledge and formal provability. Modal and modal-like languages also provide us with families of restricted description languages for relational and topological structures; they are being used in many disciplines, ranging from artificial intelligence, computer science and mathematics via natural language syntax and semantics to philosophy. (...) This volume presents a broad and up-to-date view of the field, with contributions covering both the foundations of modal logic itself and each of the aforementioned application areas. Complemented with an editorial introduction covering the roots of modal logic, this book is indispensable for any advanced student and researcher in non-classical logic and its applications. (shrink)

Modal logic is one of philosophy’s many children. As a mature adult it has moved out of the parental home and is nowadays straying far from its parent. But the ties are still there: philosophy is important to modal logic, modal logic is important for philosophy. Or, at least, this is a thesis we try to defend in this chapter. Limitations of space have ruled out any attempt at writing a survey of all the work going on in our field—a (...) book would be needed for that. Instead, we have tried to select material that is of interest in its own right or exemplifies noteworthy features in interesting ways. Here are some themes that have guided us throughout the writing: • The back-and-forth between philosophy and modal logic. There has been a good deal of give-and-take in the past. Carnap tried to use his modal logic to throw light on old philosophical questions, thereby inspiring others to continue his work and still others to criticise it. He certainly provoked Quine, who in his turn provided—and continues to provide—a healthy challenge to modal logicians. And Kripke’s and David Lewis’s philosophies are connected, in interesting ways, with their modal logic. Analytic philosophy would have been a lot different without modal logic! • The interpretation problem. The problem of providing a certain modal logic with an intuitive interpretation should not be conflated with the problem of providing a formal system with a model-theoretic semantics. An intuitively appealing model-theoretic semantics may be an important step towards solving the interpretation problem, but only a step. One may compare this situation with that in probability theory, where definitions of concepts like ‘outcome space’ and ‘random variable’ are orthogonal to questions about “interpretations” of the concept of probability. • The value of formalisation. Modal logic sets standards of precision, which are a challenge to—and sometimes a model for—philosophy. Classical philosophical questions can be sharpened and seen from a new perspective when formulated in a framework of modal logic. On the other hand, representing old questions in a formal garb has its dangers, such as simplification and distortion. • Why modal logic rather than classical (first or higher order) logic? The idioms of modal logic—today there are many!—seem better to correspond to human ways of thinking than ordinary extensional logic. (Cf. Chomsky’s conjecture that the NP + VP pattern is wired into the human brain.) In his An Essay in Modal Logic (1951) von Wright distinguished between four kinds of modalities: alethic (modes of truth: necessity, possibility and impossibility), epistemic (modes of being known: known to be true, known to be false, undecided), deontic (modes of obligation: obligatory, permitted, forbidden) and existential (modes of existence: universality, existence, emptiness). The existential modalities are not usually counted as modalities, but the other three categories are exemplified in three sections into which this chapter is divided. Section 1 is devoted to alethic modal logic and reviews some main themes at the heart of philosophical modal logic. Sections 2 and 3 deal with topics in epistemic logic and deontic logic, respectively, and are meant to illustrate two different uses that modal logic or indeed any logic can have: it may be applied to already existing (non-logical) theory, or it can be used to develop new theory. (shrink)

A cardinality result in modal propositional logic.

We investigate the research programme of dynamic doxastic logic (DDL) and analyze its underlying methodology. The Ramsey test for conditionals is used to characterize the logical and philosophical differences between two paradigmatic systems, AGM and KGM, which we develop and compare axiomatically and semantically. The importance of Gärdenfors’s impossibility result on the Ramsey test is highlighted by a comparison with Arrow’s impossibility result on social choice. We end with an outlook on the prospects and the future of DDL.

The well-known argument of Frederick Fitch, purporting to show that verificationism (= Truth implies knowability) entails the absurd conclusion that all the truths are known, has been disarmed by Dorothy Edgington''s suggestion that the proper formulation of verificationism presupposes that we make use of anactuality operator along with the standardly invoked epistemic and modal operators. According to her interpretation of verificationism, the actual truth of a proposition implies that it could be known in some possible situation that the proposition holds (...) in theactual situation. Thus, suppose that our object language contains the operatorA — it is actually the case that ... — with the following truth condition: vA iff w0, wherew 0 stands for the designated world of the model — the actual world. Then we can formalize the verificationist claim as follows. (shrink)

In 1985 Alchourrón, Gärdenfors and Makinson presented their now classic theory of theory change . In 1988 Adam Grove, generalizing David Lewis's theory of counterfactuals, presented a model theory suitable for the AGM theory. Although AGM and Grove mentioned object languages, neither used them. But recently, Maarten de Rijke has shown how object languages can be brought into the picture. In the present paper we take de Rijke's idea further, addressing the question whether there is a particular doxastic or epistemic (...) logic implicit in AGM. (shrink)

Having gained some idea of what MacIntosh logics there are, we conclude this paper with a remark about the totality of them. Let theterritory of a rule or condition be the class of all modal logics that have the rule or satisfy the condition. What is MacIntosh territory, the class of all normal logics with the MacIntosh rule, like? What is its structure?

A history of the logic of action is outlined, beginning with St Anselm. Five modern authors are discussed in some detail: von Wright, Fitch, Kanger, Chellas and Pratt.

The formal language studied in this paper contains two categories of expressions, terms and formulas. Terms express events, formulas propositions. There are infinitely many atomic terms and complex terms are made up by Boolean operations. Where and are terms the atomic formulas have the form = ( is the same as ), Forb ( is forbidden) and Perm ( is permitted). The formulae are truth functional combinations of these. An algebraic and a model theoretic account of validity are given and (...) an axiomatic system is provided for which they are characteristic.The closure principle, that what is not forbidden is permitted is shown to hold at the level of outcomes but not at the level of events. In the two final sections some other operators are considered and a semantics in terms of action games. (shrink)

This paper consists of some lecture notes in which conditional logic is treated as an extension of modal logic. Completeness and filtration theorems are provided for some basis systems.

The main purpose of the paper is to introduce philosophers and philosophical logicians to dynamic logic, a subject which promises to be of interest also to philosophy. A new completeness result involving both after — and during — operators is announced.

Dynamic doxastic logic (DDL) is used in connexion with theories of belief revision. Here we try to show that languages of DDL are suitable also for discussing aspects of default logic. One ingredient of our analysis is a concept of coherence-as-ratifiability.

We consider a quantifier-free language in which there are terms as well as formulas. The proposition-forming propositional operators are the usual ones, and the term-making term operators are the usual lattice theoretical ones. In addition there is a formula-making term operator, does. We study a new logic in which does is claimed to approximate some features of the informal concept the agent performs the action.

This paper suggests that it should be possible to develop dynamic deontic logic as a counterpart to the very successful development of dynamic doxastic logic (or dynamic epistemic logic, as it is more often called). The ambition, arrived at towards the end of the paper, is to give formal representations of agentive concepts such as “the agent is about to do (has just done) α ” as well as of deontic concepts such as “it is obligatory (permissible, forbidden) for the (...) agent to do α ”, where α stands for an action (event). (shrink)

Dynamic doxastic logic (DDL) is the modal logic of belief change. In basic DDL a modal operator [* ϕ ] carries the informal meaning "after the agent has revised his beliefs by ϕ " or "after the agent has accepted the information that ϕ "; it is assumed that the arguments of the star operator * are pure Boolean formulae. That assumption is discarded in full DDL where any pure doxastic formula may be an argument. As noted by other authors, (...) a straight-forward extension of the theory from basic DDL to full DDL invites problems of the kind first discussed by G. E. Moore. In this paper it is argued that a way to escape those problems is to redefine revision in a way that seems appropriate for this semantically richer context. The paper deals only with the one-agent case, but the approach can be extended to the case of multiple agents. (shrink)

We define prenormal modal logics and show that S1, S1, S0.9, and S0.9 are Lewis versions of certain prenormal logics, determination and decidability for which are immediate. At the end we characterize Cresswell logics and ponder C. I. Lewis's idea of strict implication in S1.