Counterpart-Theoretic Semantics for Modal Logic

Hazen, Allen

doi:10.2307/2025472

Cited by 147 publications

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“…26 Hazen (1979) uses something similar to multi-centered worlds in giving a counterparttheoretic semantics for a language of quantified modal logic that includes an actuality operator. Proposals closely related to Hazen's are discussed in Dorr 2010, Stalnaker 2012, Bacon forthcoming, Kment forthcoming, and Russell forthcoming.…”

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confidence: 99%

Counterfactual attitudes and multi-centered worlds

Ninan

2012

S&P

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Counterfactual attitudes like imagining, dreaming, and wishing create a problem for the standard formal semantic theory of de re attitude ascriptions. I show how the problem can be avoided if we represent an agent's attitudinal possibilities using multi-centered worlds, possible worlds with multiple distinguished individuals, each of which represents an individual with whom the agent is acquainted. I then present a compositional semantics for de re ascriptions according to which singular terms are assignmentsensitive expressions and attitude verbs are assignment shifters.

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Counterfactual attitudes and multi-centered worlds

Ninan

2012

S&P

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“…However, Kripke does use the example of proper names of persons to make a case against Lewis's anti-branching, divergence-based counterpart theory for de re modality, most famously via his example of U.S. presidential candidate Humphrey, who "couldn't care less whether someone else, no matter how much resembling him, would have been victorious in another possible world" (Kripke 1980, 45n13). [The point remains contentious; cf., e.g., Hazen (1979) and Mackie (2008). ]…”

Section: Branching In (Of?) Timementioning

confidence: 99%

Branching in the landscape of possibilities

Müller

2012

Synthese

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The metaphor of a branching tree of future possibilities has a number of important philosophical and logical uses. In this paper we trace this metaphor through some of its uses and argue that the metaphor works the same way in physics as in philosophy. We then give an overview of formal systems for branching possibilities, viz., branching time and (briefly) branching space-times. In a next step we describe a number of different notions of possibility, thereby sketching a landscape of possibilities. In the final section of the paper we look at the place of branching-based possibilities in that larger landscape of possibilities. Our main message is that far from being an outlandish metaphysical extravagancy, branching-based possibilities are epistemically as well as metaphysically basic.Keywords Branching time · Branching space-times · Modality · Possibility · ExperimentThe metaphor of branching is useful for describing a certain type of modality: an open future can be pictured as a branching tree of concrete possibilities. In this paper we will look at the place of branching-based possibilities in the larger landscape of possibilities. The main message is that far from being an outlandish metaphysical extravagancy, branching-based possibilities are absolutely basic.The paper is structured as follows: In Sect. 1 we trace the branching metaphor through some of its uses and argue that the uses in philosophy and in the sciences are of a piece. In Sect. 2 we briefly describe two formal frameworks for branching-based possibilities, branching time and branching space-times. Section 3 centers on the notion of a scientific experiment to motivate different types of possibilities, thereby giving

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“…While it is obvious that a closed formula should be valued as the set of states where it holds, consider instead the open formula source(edge) = target(edge) ∨ ♦Z: once the value of edge is chosen in the current state, how is such value passed to the states denoted by the fix-point variable Z? The issue is denoted in the quantified temporal logic literature as the trans-world identity problem (see [15] as well as [2] for a survey of the related philosophical issues). From a practitioner point of view, a typical solution follows the so-called "Kripke semantics" approach: roughly, a set of universal (graph) items is chosen, and its elements are used to form each state.…”

Section: Introductionmentioning

confidence: 99%

Counterpart Semantics for a Second-Order μ-Calculus

Gadducci

Lafuente

Vandin

2010

Lecture Notes in Computer Science

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Abstract. We propose a novel approach to the semantics of quantified µ-calculi, considering models where states are algebras; the evolution relation is given by a counterpart relation (a family of partial homomorphisms), allowing for the creation, deletion, and merging of components; and formulas are interpreted over sets of state assignments (families of substitutions, associating formula variables to state components). Our proposal avoids the limitations of existing approaches, usually enforcing restrictions of the evolution relation: the resulting semantics is a streamlined and intuitively appealing one, yet it is general enough to cover most of the alternative proposals we are aware of.

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Counterpart-Theoretic Semantics for Modal Logic

Cited by 147 publications

References 0 publications

Counterfactual attitudes and multi-centered worlds

Counterfactual attitudes and multi-centered worlds

Branching in the landscape of possibilities

Counterpart Semantics for a Second-Order μ-Calculus

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