Natural language provides motivation for studying modal backwards-looking operators such as “now”, “then” and “actually” that evaluate their argument formula at some previously considered point instead of the current one. This paper investigates the expressive power over models of both propositional and first-order basic modal language enriched with such operators. Having defined an appropriate notion of bisimulation for first-order modal logic, I show that backwards-looking operators increase its expressive power quite mildly, contrary to beliefs widespread among philosophers of language and formal semanticists. That in turn presents a strong argument for the use of operator-based systems in the semantics of natural language, instead of systems with explicit quantification over worlds and times that have become a de-facto standard for such applications. The popularity of such explicit-quantification systems is shown to be based on the misinterpretation of a claim by Cresswell, which led many philosophers and linguists to assume that introducing “now” and “then” is expressively equivalent to explicitly quantifying over worlds and times
Keywords “Now” operator  Backwards-looking operators  Bisimulation  First-order modal logic  Hybrid logic
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DOI 10.1007/s10849-014-9210-3
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References found in this work BETA

Counterpart Theory and Quantified Modal Logic.David K. Lewis - 1968 - Journal of Philosophy 65 (5):113-126.
Formal Properties of 'Now'.Hans Kamp - 1971 - Theoria 37 (3):227-273.
A Plea for Monsters.Philippe Schlenker - 2002 - Linguistics and Philosophy 26 (1):29-120.

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Citations of this work BETA

Logic Talk.Alexander W. Kocurek - 2021 - Synthese 199 (5-6):13661-13688.
The Problem of Cross-World Predication.Alexander Kocurek - 2016 - Journal of Philosophical Logic 45 (6):697-742.
Looking Backwards in Type Logic.Jan Köpping & Thomas Ede Zimmermann - 2021 - Inquiry: An Interdisciplinary Journal of Philosophy 64 (5-6):646-672.

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