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Showing papers on "Modal operator published in 2003"


Journal ArticleDOI
TL;DR: This paper studies finitary modal logics, interpreted over coalgebras for an endofunctor, and establishes soundness, completeness and decidability results, and believes that this induction principle also opens new ways for reasoning about modal logs.

179 citations


Journal ArticleDOI
Churn-Jung Liau1
TL;DR: By use of modal logic, the relationship among belief, information acquisition and trust is semantically and axiomatically characterized and the applications of the logic to computer security and database reasoning are suggested.

160 citations


Journal ArticleDOI
TL;DR: This work investigates the topological interpretation of modal logic in modern terms, using a new notion of bisimulation, and presents a new proof of McKinsey and Tarski’s theorem on completeness of S4 with respect to the real line and a completeness proof for the logic of finite unions of convex sets of reals.
Abstract: We investigate the topological interpretation of modal logic in modern terms, using a new notion of bisimulation. We look at modal logics with interesting topological content, presenting, among others, a new proof of McKinsey and Tarski’s theorem on completeness of S4 with respect to the real line, and a completeness proof for the logic of finite unions of convex sets of reals. We conclude with a broader picture of extended modal languages of space, for which the main logical questions are still wide open.

118 citations


BookDOI
01 Jan 2003
TL;DR: It is argued that policy-based intentions exhibit non-monotonic behaviour which could be captured through a non-Monotonic system like defeasible logic, which alleviates most of the problems related to logical omniscience.
Abstract: Most of the theories on formalising intention interpret it as a unary modal operator in Kripkean semantics, which gives it a monotonic look. We argue that policy-based intentions(Bratman 1990) exhibit non-monotonic behaviour which could be captured through a non-monotonic system like defeasible logic. To this end we outline a defeasible logic of intention. The proposed technique alleviates most of the problems related to logical omniscience. The proof theory given shows how our approach helps in the maintenance of intention-consistency in agent systems like BDI.

70 citations


Journal Article
TL;DR: A modal logic of probability with a unary modal operator expressing that a proposition is more probable than its negation that focuses on the evolution of belief, and proposes an integration of revision.
Abstract: We investigate a modal logic of probability with a unary modal operator expressing that a proposition is more probable than its negation Such an operator is not closed under conjunction, and its modal logic is therefore non-normal Within this framework we study the relation of probability with other modal concepts: belief and action We focus on the evolution of belief, and propose an integration of revision For that framework we give a regression algorithm

30 citations


Book ChapterDOI
01 Jan 2003
TL;DR: The notion of epistemic logics of knowledge and belief has been introduced in this paper, where the authors follow the tradition of most recent treatments of modal logics, including those of belief and knowledge, by adopting possible world semantics in the style of Kripke.
Abstract: Knowledge has always been a topic central to philosophy (cf. e.g. [Glymour, 1992]). Since ancient times philosophers have been interested in the way knowledge comes to us and in what way it relates to reality, the world in which we live. As is the case with so many things, during this century also the topic of knowledge has become the subject of formal investigations. Questions arose such as what the logical properties of knowledge are, and in order to come up with answers to these, logics have been devised to study these questions in a formal setting. These logics are now generally called ‘epistemic logics’, i.e., logics pertaining to ‘knowledge’. Mostly, also the notion of ‘belief, which is sometimes thought of as a weaker form of knowledge (but this is debated among philosophers (cf. [Gettier, 1963; Pollock, 1986; Voorbraak, 1993]) is considered, and we will also incorporate this notion in our treatment. Sometimes logics of belief are referred to with the special term ‘doxastic logics’, but we will just use the term ‘epistemic logic(s)’ for logics of knowledge and belief. Jaakko Hintikka [1962] was the first who proposed a modal logic approach to knowledge and belief. We follow the tradition of most recent treatments of modal logics, including those of knowledge and belief, by adopting possible world semantics in the style of Kripke [1963].

27 citations


Journal Article
TL;DR: A fixpoint semantics and an SLD-resolution calculus for MProlog in all of the basic serial modal logics KD, T, KDB, B, KD4, S4, KD5, KD45, and S5 are given.
Abstract: We propose a modal logic programming language called MProlog, which is as expressive as the general modal Horn fragment. We give a fixpoint semantics and an SLD-resolution calculus for MProlog in all of the basic serial modal logics KD, T, KDB, B, KD4, S4, KD5, KD45, and S5. For an MProlog program P and for L being one of the mentioned logics, we define an operator T_{L,P}, which has the least fixpoint I_{L,P}. This fixpoint is a set of formulae, which may contain labeled forms of the modal operator d, and is called the least L-model generator of P. The standard model of I_{L,P} is shown to be a least L-model of P. The SLD-resolution calculus for MProlog is designed with a similar style as for classical logic programming. It is sound and complete. We also extend the calculus for MProlog in the almost serial modal logics KB, K5, K45, and KB5.

24 citations


Proceedings ArticleDOI
27 Aug 2003
TL;DR: A typed, purely functional calculus for state (with second-class locations) in which types reflect the dichotomy between reading from and writing into the global store, in contrast to the usual formulation of state via monads.
Abstract: In this paper we propose a typed, purely functional calculus for state (with second-class locations) in which types reflect the dichotomy between reading from and writing into the global store. This is in contrast to the usual formulation of state via monads, where the primitives for reading and writing introduce the same monadic type constructor. We hope to argue that making this distinction is useful, simple, and has strong logical foundations.Our type system is based on the proof-term calculus for constructive modal logic S4, which has two modal type operators: ␣ for necessity and ◊ for possibility. We extend this calculus with the notion of names (which stand for locations) and generalize to indexed families of modal operators (indexed by sets of names). Then, the modal type ␣CA classifies computations of type A which read from store locations listed in the set C. The dual type ␣CA classifies computations which first write into the locations from $C$ and than use the changed store to obtain a value of type A.There are several benefits to this development. First, the necessitation fragment of the language is interesting in its own: it formulates a calculus of dynamic binding. Second, the possibility operator ◊ is a monad, thus forcing the single-threading of memory writes, but not of memory reads (as these are associated with ␣). Finally, the different status of reads and writes gives rise to a natural way of expressing the allocation of uninitialized memory while also providing guarantees that only initialized locations are dereferenced.

22 citations


Journal ArticleDOI
TL;DR: In this paper, some of the most important essays in the metaphysics of modality are collected, dating back from the late 1960's to the present, which chronicle the development of Plantinga's thoughts about some fundamental issues in metaphysics: what is the nature of abstract objects like possible worlds, properties, propositions, and such phenomena? Can objects that do not exist exemplify properties?
Abstract: Perhaps no one has done more in the last 30 years to advance thinking in the metaphysics of modality than has Alvin Plantinga. Collected here are some of his most important essays on this influential subject. Dating back from the late 1960's to the present, they chronicle the development of Plantinga's thoughts about some of the most fundamental issues in metaphysics: what is the nature of abstract objects like possible worlds, properties, propositions, and such phenomena? Are there possible but non-actual objects? Can objects that do not exist exemplify properties? Plantinga gives thorough and penetrating answers to all of these questions and many others. This volume contains some of the best work in metaphysics from the past 30 years, and will remain a source of critical contention and keen interest among philosophers of metaphysics and philosophical logic for years to come.... Download ebook, read file pdf Essays in the Metaphysics of Modality

15 citations


Journal ArticleDOI
TL;DR: The AGM theory of belief change is introduced and to exemplify the diversity and significance of the research that has been inspired by the AGM article in the last 25 years is exemplified.
Abstract: This thesis consists in six articles and a comprehensive summary. • The pourpose of the summary is to introduce the AGM theory of belief change and to exemplify the diversity and significance of the research that has been inspired by the AGM article in the last 25 years. The research areas associated with AGM was divided in three parts: criticisms, where we discussed some of the more common criticisms of AGM. Extensions where the most common extensions and variations of AGM are presented and applications where we provided an overview of applications and connections with other areas of research. • Article I elaborates on the connection between partial meet contractions [AGM85] and kernel contractions [Han94a] in belief change theory. Also both functions are equivalent in belief sets, there are notequivalent in belief bases. A way to define incision functions (used in kernel contractions) from selection functions (used in partial meet contractions) and vice versa is presented. It is explained under which conditions there are exact correspondences between selection and incision functions so that the same contraction operations can be obtained by using either of them. • Article II proposes an axiomatic characterization for ensconcement-based contraction functions, belief base functions proposed byWilliams and relates this function with other kinds of base contraction functions. • Article III adapts the Ferme and Hansson model of Shielded Contraction [FH01] as well as Hansson et all Credibility-Limited Revision [HFCF01] for belief bases, to join two of the many variations of the AGM model [AGM85], i.e. those in which knowledge is represented through belief bases instead of logic theories, and those in which the object of the epistemic change does not get the priority over the existing information as it is the case in the AGM model. • Article IV introduces revision by comparison a refined method for changing beliefs by specifying constraints on the relative plausibility of propositions. Like the earlier belief revision models, the method proposed is a qualitative one, in the sense that no numbers are needed in order to specify the posterior plausibility of the new information. The method uses reference beliefs in order to determine the degree of entrenchment of the newly accepted piece of information. Two kinds of semantics for this idea are proposed and a logical characterization of the new model is given. • Article V focuses on the extension of AGM that allows change for a belief base by a set of sentences instead of a single sentence. In [FH94], Fuhrmann and Hansson presented an axiomatic for Multiple Contraction and a construction based on the AGM Partial Meet Contraction. This essay proposes for their model another way to construct functions: Multiple Kernel Contraction, that is a modification of Kernel Contraction,proposed by Hansson [Han94a] to construct classical AGM contractions and belief base contractions. • Article VI relates AGM model with the DFT model proposed by Carlos Alchourron [Alc93]. Alchourron devoted his last years to the analysis of the notion of defeasible conditionalization. His definition of the defeasible conditional is given in terms of strict implication operator and a modal operator f which is interpreted as a revision function at the language level. This essay points out that this underlying revision function is more general than AGM revision. In addition, a complete characterization of that more general kind of revision that permits to unify models of revision given by other authors is given.

14 citations


Journal ArticleDOI
TL;DR: The invariance theorem is proved, which is the formal dual of Birkhoff's completeness theorem, and shows how closure under deductive rules dualises to yield two modal operators acting on coequations.
Abstract: We present the dual to Birkhoff's variety theorem in terms of predicates over the carrier of a cofree coalgebra (that is, in terms of ‘coequations’). We then discuss the dual to Birkhoff's completeness theorem, showing how closure under deductive rules dualises to yield two modal operators acting on coequations. We discuss the properties of these operators and show that they commute. We prove as our main result the invariance theorem, which is the formal dual of Birkhoff's completeness theorem.

Proceedings ArticleDOI
26 Aug 2003
TL;DR: The proposal is to treat meta-variables as modal variables in a modal type theory, which is logically clean and justifies several low-level implementation techniques for meta-Variables.
Abstract: We report on work in progress regarding a foundation for the notion of meta-variable in logical frameworks and type theories. Our proposal is to treat meta-variables as modal variables in a modal type theory, which is logically clean and justifies several low-level implementation techniques for meta-variables. We also speculate on other logical extensions of our modal type theory, at present without clear applications.

Journal ArticleDOI
Maria Fasli1
TL;DR: This paper presents an alternative framework for formal theories of agents which is di¤erent from those found in the literature in two ways: Firstly, a syntactical approach for the representation of the propositional attitudes is adopted, and secondly, the relation between knowledge and belief is thoroughly explored.
Abstract: The study of formal theories of agents has intensi…ed over the last couple of decades, since such formalisms can be viewed as providing the speci…cations for building rational agents and multi-agent systems. Most of the proposed approaches are based upon the well-understood framework of modal logics and possible world semantics. Although intuitive and expressive, these approaches lack two properties that can be considered important to a rational agent’s reasoning: quanti…cation over the propositional attitudes, and self-referential statements. This paper presents an alternative framework which is di¤erent from those found in the literature in two ways: Firstly, a syntactical approach for the representation of the propositional attitudes is adopted. This involves the use of a truth predicate and syntactic modalities which are de…ned in terms of the truth predicate itself and corresponding modal operators. Secondly, an agent’s information state includes both knowledge and beliefs. Independent modal operators for the two notions are introduced and based on them syntactic modalities are de…ned. Furthermore, the relation between knowledge and belief is thoroughly explored and three di¤erent connection axiomatisations for the modalities and the syntactic modalities are proposed and their properties investigated.

Book ChapterDOI
02 Jul 2003
TL;DR: A simple modal logic of probability with a unary modal operator expressing that a proposition is more probable than its negation is investigated, which is not closed under conjunction, and itsmodal logic is therefore non-normal.
Abstract: We investigate a simple modal logic of probability with a unary modal operator expressing that a proposition is more probable than its negation. Such an operator is not closed under conjunction, and its modal logic is therefore non-normal. Within this framework we study the relation of probability with other modal concepts: belief and action.

01 Jan 2003
TL;DR: A general framework for effect handling systems is developed, and novel calculi for exceptions, catch-and-throw and composable continuations as specific instantiations are obtained.
Abstract: In their purest formulation, monads are used in functional programming for two purposes: (1) to hygienically propagate effects, and (2) to globalize the effect scope once an effect occurs, the purity of the surrounding computation cannot be restored. As a consequence, monadic typing does not provide very naturally for the practically important ability to handle effects, and there is a number of previous works directed toward remedying this deficiency. It is mostly based on extending the monadic framework with further extra-logical constructs to support handling. In this paper we adopt a different approach, founded on the observation of Pfenning and Davies that an abstract monad can be decomposed in terms of modal operators for possibility O and necessity D. Our idea is to use the • modality (which is a comonad) for hygienic propagation of effects, and leave the globalization of effect scope to O. Then the effects which admit a natural notion of handling can be encoded using • ; since they are not global, there is no need to push them under O. Based on this idea, we develop a general framework for effect handling systems, and obtain novel calculi for exceptions, catch-and-throw and composable continuations as specific instantiations.

Book ChapterDOI
TL;DR: A formal language for multi-agent systems based on new modal operators that express concurrency at the syntactic level and applies game-theory to interpret the quantified modalities and to determine which information is available to the agents as well as their reasoning capabilities.
Abstract: We introduce a formal language for multi-agent systems based on new modal operators. The modal operators express concurrency at the syntactic level. Operators containing quantifiers describe the evolution of a system where each agent has knowledge of other agents' attitude toward a goal but not of their actions. This result is obtained without introducing standard epistemic operators. The semantics presents a mixture of Tarskian and game-theoretical elements. We apply game-theory to interpret the quantified modalities and to determine which information is available to the agents as well as their reasoning capabilities.

Journal ArticleDOI
TL;DR: This paper introduces a class of LA-logics with a countably infinite set of modal indices and shows that the satisfiability problem is PSPACE-complete for every logic of such a class and establishes a surprising correspondence between the modal depth of formulae and the number of occurrences of distinct modal connectives.

Dissertation
01 Jan 2003
TL;DR: This dissertation is intended to provide a formalism for those generics that trigger nonmonotonic inferences to reflect intentionality and exception-tolerating features of generics, and has an emphasis on the axiomatization of generic reasoning that encodes nonmonotonicity.
Abstract: This dissertation is intended to provide a formalism for those generics that trigger nonmonotonic inferences. The formalism is to reflect intentionality and exception-tolerating features of generics, and has an emphasis on the axiomatization of generic reasoning that encodes nonmonotonicity. A modal conditional approach is taken to formalize the nonmonotonic reasoning in general at the level of object language. A serial of logic systems—MN, NID, NCUM, N STCUM—are constructed in an increasing strength of the characterized nonmonotonic inference relation. In these systems, two binary modal operators g and > are introduced in their syntax, and a o function lifted from the traditional ∗ function is deployed in their semantics. These systems are shown to be sound and complete with respect to certain classes of frames defined in the semantics. They are decidable as well. The nonmonotonic inference is argued to be a ternary relation “[Φ], Γ |∼ α”, and is defined in the system NSTCUM. Many widely discussed nonmonotonic inference patterns such as Defeasible Modus Ponens, Defeasible Transitivity, the Penguin Principle etc. are justified. The specificity rule is proved to be a theorem of the system N STCUM. The impact of negated defaults on an inference is also investigated and accounted for. A canonical form to read off generics is proposed: All generic sentences with subject-predicate (SP) structure can be re-written into their canonical form S (normally P). If S is a plural noun phrase, it can be further refined to be (normal S) (normally P). Normal objects are selected based on the “meaning” of the subject and predicate terms. The second parameter provides an aspect with respect to which certain objects of a kind are considered normal. Due to such a way to select normal objects, the drowning problem is solved. The inference behaviors of generics are axiomatized in the system G, which is a quantificational extension of the system NSTCUM. It is proved to be sound and complete with respect to the class of Lg,G -frames. Those benchmark examples of generic inferences are examined in the system G.

Journal ArticleDOI
TL;DR: In this paper, it has been suggested that the Modal Interpretation of Quantum Mechanics (QM) is "incomplete" if it lacks a dynamics for possessed values, which is only one of two possible attitudes one might adopt toward a modal interpretation without dynamics.
Abstract: It has been suggested that the Modal Interpretation of Quantum Mechanics (QM) is "incomplete" if it lacks a dynamics for possessed values. I argue that this is only one of two possible attitudes one might adopt toward a Modal Interpretation without dynamics. According to the other attitude, such an interpretation is a complete interpretation of QM as standardly formulated, an interpretation whose innovation is to attempt to make sense of the quantum realm without the expedient of novel physics. Then I explain why this attitude, though available, is unattractive. Without dynamics, the Modal Interpretation vanquishes the measurement problem only, it seems, to succumb to the problem of state preparation. On this view, the Modal Interpretation needs dynamics not to be an interpretation at all, but to be an adequate one. I review reasons to suspect that the dynamics which would best suit the Modal Interpretation--a dynamics equivalent to a set of two time transition probabilities of the sort used to solve the ...

Book ChapterDOI
TL;DR: This study provides an algebraic background for the formal derivation of greedy-like algorithms and proposes Kleene algebra as a particularly simple alternative to previous approaches such as relation algebra, using modal operators that are definable in a wide class of algebras, based on domain/codomain or image/pre-image operations.
Abstract: This study provides an algebraic background for the formal derivation of greedy-like algorithms. We propose Kleene algebra as a particularly simple alternative to previous approaches such as relation algebra. Instead of converse and residuation we use modal operators that are definable in a wide class of algebras, based on domain/codomain or image/pre-image operations. By abstracting from earlier approaches we arrive at a very general theorem about the correctness of loops that covers particular forms of greedy algorithms as special cases.

Proceedings ArticleDOI
02 Nov 2003
TL;DR: A novel possible world semantics for intention is introduced, called the twin-subset semantics, which describes the intentions of agent in a possible world w with two subsets of W, where W is the set of all possible worlds which an agent can be in.
Abstract: Intention, an indispensable cognition attribute of agent, plays an important role in agent's rational behavior. There is a lot of research on formalization of cognitive state that include intentions of the agents in a multi-agent system. These theories are based on normal modal logic, interpret intention as unary normal modal operator in Kripke semantics, and hence suffer from the harmful logical omniscience and side-effect problems. These have not been eliminated satisfactorily as yet. In this paper, we interpret intention as unary non-normal modal operator and introduce novel possible world semantics for intention, called the twin-subset semantics. It describes the intentions of agent in a possible world w with two subsets of W, where W is the set of all possible worlds which an agent can be in, and allows us to embody essential cognitive features of intention and the relations between belief and intention. Compared with classical normal or non-normal modal logics, not only does it avoid the logical omniscience and side-effect problems but also the classical semantics of logical connectives are still valid; and moreover, it improves the true-false subset semantics, which were introduced by us previously, and overcomes its serious drawbacks.

Proceedings Article
09 Aug 2003
TL;DR: This paper shows that the results of des Rivieres & Levesque and Morreau & Kraus fit nicely into the framework of logic programming semantics, in that they are shown to be corollaries of well-known results in this field.
Abstract: This paper concerns formal theories for reasoning about the knowledge and belief of agents. It has seemed attractive to researchers in artificial intelligence to formalise these propositional attitudes as predicates of first-order predicate logic. This allows the agents to express stronger introspective beliefs and engage in stronger meta-reasoning than in the classical modal operator approach. Results by Montague [1963] and Thomason [1980] show, however, that the predicate approach is prone to inconsistency. More recent results by des Rivieres & Levesque [1988] and Morreau & Kraus [1998] show that we can maintain the predicate approach if we make suitable restrictions to our set of epistemic axioms. Their results are proved by careful translations from corresponding modal formalisms. In the present paper we show that their results fit nicely into the framework of logic programming semantics, in that we show their results to be corollaries of well-known results in this field. This does not only allow us to demonstrate a close connection between consistency problems in the syntactic treatment of propositional attitudes and problems in semantics for logic programs, but it also allows us to strengthen the results of des Rivieres & Levesque [1988] and Morreau & Kraus [1998].

Book ChapterDOI
TL;DR: A Rasiowa-Sikorski proof system is presented for an elementary set theory which can act as a target language for translating propositional modal logics and enables a fine-tunable and uniform analysis of modal deductions in a simple and purely set-theoretic language.
Abstract: A Rasiowa-Sikorski proof system is presented for an elementary set theory which can act as a target language for translating propositional modal logics. The proposed system permits a modular analysis of (modal) axioms in terms of deductive rules for the relational apparatus. Such an analysis is possible even in the case when the starting modal logic does not possess a first-order correspondent. Moreover, the formalism enables a fine-tunable and uniform analysis of modal deductions in a simple and purely set-theoretic language.

01 Jan 2003
TL;DR: CO3L is a compact, expressive and easy to use language for ontology representation based on the language of the first order logic, with explicit world states and the relational operator State/1, which is true of world state designators.
Abstract: This paper presents CO3L, a compact, expressive and easy to use language for ontology representation. CO3L reflects the O3F model of ontology representation proposed elsewhere. The proposed language enables the representation of basic ontological entities, their relationships, and arbitrary axioms of the domain. Ontological entities include classes, properties, methods, facets and types. Relationships include n-ary associations and inheritance. Axioms may be used to capture complex constraints and relations between entities, to define relational and functional methods, and to represent the effects of the execution of action methods in the world. CO3L is based on the language of the first order logic, with explicit world states; the relational operator State/1, which is true of world state designators; the functional operator Do/2, which returns the world state designator resulting of the execution of an action in a given world state; and the modal operator Holds/2 which is true of propositions satisfied in given world states.

Book ChapterDOI
TL;DR: A Situation Event Logic is proposed, an extension of modal logic, in which modal operators have a well defined scope over a set of situations and this logic is used to represent and infer knowledge from the environment and agent diagrams.
Abstract: Nowadays agent-oriented software engineering methodologies emphasize the importance of the environment in which a multiagent system (MAS) operate. Meanwhile, they do not propose any diagram to represent the environment and its effects on the MAS. So, we propose two diagrams that can be introduced in agent-oriented methodologies: an environment diagram representing environment evolution over time, and an agent diagram showing the MAS organization according to the agents' roles and their relationships. Furthermore, many model checking techniques were defined to validate whether a MAS will solve the problem for which it is designed. However, these techniques do not consider the environment in their checking procedure. We propose a Situation Event Logic, an extension of modal logic, in which modal operators have a well defined scope over a set of situations. This logic is used to represent and infer knowledge from the environment and agent diagrams.


Journal ArticleDOI
01 Dec 2003
TL;DR: In this article, the authors defend causal explanation of modal intuitions and judgments, and argue that causal explanation does not undermine rational trust in them and that trust and explanation support each other.
Abstract: The paper defends causal explanationism concerning our modal intuitions and judgments, and, in particular, the following claims. If a causally explainable mirroring or “pre-established harmony” between our mind and modal reality obtains, we are justified in believing it does. We do not hold our modal beliefs compulsively and blindly but with full subjective and objective justification. Therefore, causal explanation of our modal beliefs does not undermine rational trust in them. Explanation and trust support each other. In contrast, anti-explanationists (from Kant, through neo-wittgensteinians to T. Nagel and J. Pust), claim that causal explanation of intuitions and judgments undermines rational trust in them. They especially target causal explanation in terms of pre-established harmony between our mind, shaped by causal processes, and the underlying modal structure of reality. The paper argues against them. The argument builds upon the claim that the appeal to modal facts is indispensable for systematization and explanation of non-modal ones. Therefore, we should assume that modal facts exist and are not disjoint and isolated from actual facts. The modal structure of the universe intervenes in the non-modal reality. Causal processes indirectly carry information about deep modal structure. Any (reasonable candidate) causal explanation of our intuitional modal beliefs should start from this indirect contact with and information about modal facts. Therefore, if our intuitional modal beliefs are true and causally explainable (by a factual, non-modal explanans), they are true in virtue of the deep underlying modal structure. They are sensitive to modal reality and track it. We can come to know this fact, and thus strengthen our spontaneous trust in our modal intuitions.

Journal ArticleDOI
TL;DR: A compositional version of the fictionalist strategy is developed and critiqued, and some general semantic morals are drawn from the failures of both strategies.
Abstract: Modal fictionalists propose to defuse the unwanted ontological commitments of modal realism by treating modal realism as a fictional story, and modal assertions as assertions, prefixed by a fictionalist operator, that something is true in that story. However, consideration of conditionals with modal antecedents raises the problem ofembedding, which shows that the simple prefixing strategy cannotsucceed. A compositional version of the fictionalist strategy isdeveloped and critiqued, and some general semantic morals aredrawn from the failures of both strategies.

Proceedings Article
01 Jan 2003
TL;DR: In this article, a detailed analysis of very weak fragments of modal logic is presented, which lack connectives that introduce non-determinism and feature restrictions on the modal operators, leading to substantial reductions in complexity.
Abstract: We provide a detailed analysis of very weak fragments of modal logic. Our fragments lack connectives that introduce non-determinism and they feature restrictions on the modal operators, which may lead to substantial reductions in complexity. Our main result is a general game-based characterization of the expressive power of our fragments over the class of nite structures.