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In this section I'll discuss the approach taken by most computer scientists, who, unlike McCarthy, use a modal language to formalize propositional attitudes.
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The hybridization of a modal language amounts to extending its expressive power in such a way that it becomes possible to refer in the object language to a particular state of the model (see e.g., Blackburn 2000).
These results typically devise a modal logical language to describe games in strategic form, typically including modalities for the players' actions and preference, and show that the notion of profile being a Nash Equilibrium language is definable in such a language.
The logical consequences for no-trace actualists, however, appear to be severe; at the least they cannot provide a standard compositional semantics for modal languages, according to which (roughly) the meaning of a sentence is determined by its logical form and the meanings of its semantically significant constituents.
The modal language here does not seem to help resolving this issue.
In order to be able to speak in a modal language about important distinctions between theories, researchers have extended provability logic in many different ways.
With these epistemic relations in place, the expanded classification A can be used to interpret a basic modal language.
In fact, new actualists generally tend to opt for fixed domain semantics for modal logic (as discussed briefly in note 6 above) and a modal language that contains a dedicated predicate 'C!' to express the property of concreteness.
The key insight in Kripke's (first-order) quantified modal logic is the replacement of the single domain D of individuals in the interpretation of a first-order modal language with a function dom that assigns to each world w of the interpretation its own distinct domain of individuals dom(w).
The authors focus on the use of modal languages as tools to analyze the properties of relational structures, including their algorithmic and algebraic aspects.
There are at least two questions to be asked about this approach to the semantics of ability attributions, and of modal language more generally.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com