Expressivity of Second Order Propositional Modal Logic

Cate, Balder ten

doi:10.1007/s10992-005-9012-9

Cited by 16 publications

(3 citation statements)

References 15 publications

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“…The decidability of follows as a special case; this establishes the last outstanding claim presented in Figure 1. This decidability result in the unimodal case was already noted by ten Cate [8, p. 222]. ten Cate also observes that the corresponding monadic second-order theory is undecidable as long as .…”

Section: Multimodal Logicssupporting

confidence: 71%

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Axiomatizability of Propositionally Quantified Modal Logics on Relational Frames

Fritz¹

2022

J. symb. log.

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Propositional modal logic over relational frames is naturally extended with propositional quantifiers by letting them range over arbitrary sets of worlds of the relevant frame. This is also known as second-order propositional modal logic. The propositionally quantified modal logic of a class of relational frames is often not axiomatizable, although there are known exceptions, most notably the case of frames validating the strong modal logic $\mathrm {S5}$ . Here, we develop new general methods with which many of the open questions in this area can be answered. We illustrate the usefulness of these methods by applying them to a range of examples, which provide a detailed picture of which normal modal logics define classes of relational frames whose propositionally quantified modal logic is axiomatizable. We also apply these methods to establish new results in the multimodal case.

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Section: Multimodal Logicssupporting

confidence: 71%

“…This highlights that despite the existence of the backwards translation on transitive frames, is in general less expressive than . For more on questions of expressivity, see [8].…”

Section: Multimodal Logicsmentioning

confidence: 99%

Axiomatizability of Propositionally Quantified Modal Logics on Relational Frames

Fritz¹

2022

J. symb. log.

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“…In a completely non-technical paper [20], we also saw perhaps the earliest proposal of treating ∀p as quantifying directly over objects in a lattice of propositions, a proposal perhaps inspired by the philosophical stance defended in that paper. Since then, there has been a steady stream of interest devoted to this topic, with general theoretical results focusing on expressive power under the standard possible-world semantics ( [21][22][23][24]), specific results mostly establishing non-axiomatizability ( [25][26][27][28][29][30][31][32][33]) with the exception of [31] and [33], and more application-oriented works: [1,[34][35][36][37][38][39].…”

Section: Axiomatizability For Modal Logics With Propositional Quantifiersmentioning

confidence: 99%

On the Logic of Belief and Propositional Quantification

Ding

2021

J Philos Logic

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We consider extending the modal logic KD45, commonly taken as the baseline system for belief, with propositional quantifiers that can be used to formalize natural language sentences such as “everything I believe is true” or “there is something that I neither believe nor disbelieve.” Our main results are axiomatizations of the logics with propositional quantifiers of natural classes of complete Boolean algebras with an operator (BAOs) validating KD45. Among them is the class of complete, atomic, and completely multiplicative BAOs validating KD45. Hence, by duality, we also cover the usual method of adding propositional quantifiers to normal modal logics by considering their classes of Kripke frames. In addition, we obtain decidability for all the concrete logics we discuss.

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Hybrid Logic Meets IF Modal Logic

Tulenheimo

2009

J of Log Lang and Inf

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Expressivity of Second Order Propositional Modal Logic

Cited by 16 publications

References 15 publications

Axiomatizability of Propositionally Quantified Modal Logics on Relational Frames

Axiomatizability of Propositionally Quantified Modal Logics on Relational Frames

On the Logic of Belief and Propositional Quantification

Hybrid Logic Meets IF Modal Logic

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