Propositional Modal Logic with Implicit Modal Quantification

Padmanabha, Anantha; Ramanujam, R.

doi:10.1007/978-3-662-58771-3_2

Cited by 8 publications

(10 citation statements)

References 21 publications

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“…This latter notion is worthwhile defining explicitly, as this will open the door to a reinterpretation of epistemic logic with names in neighborhood semantics. This definition turns out to be essentially of the same shape as in [22], but taking into account the naming function. Definition 6.…”

Section: Morphisms and Bisimulationsmentioning

confidence: 99%

“…These assumptions being controversial anyway [31,27], this raises the question of whether the logic AX N is sound and complete with respect to a larger class of frames. The completeness result provided in [22] provides evidence that this is the case, but a precise argument for this was still missing. Definition 7.…”

Section: Neighborhood Semanticsmentioning

confidence: 99%

“…The first part is standard, and proceeds by induction on the complexity of the formula ϕ. For the second part, the proof follows the argument in [22].…”

Section: Lemma 2 Assume B Is a Bisimulation Between A Model M And A M...mentioning

confidence: 99%

“…That paper, however, does not address questions of definability, invariance, expressive power, or proof theory. [22] makes headway in that direction for a very closely related, but still non-equivalent language.…”

mentioning

confidence: 99%

“…The modality S is close to a modality considered in[22], only the one used in[22] quantifies globally over all agents in A, not only those that exist in a particular state. It is not expressible in epistemic logic with names either.…”

mentioning

confidence: 99%

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Revisiting Epistemic Logic with Names

Bílková

Christoff

Roy

2021

Electron. Proc. Theor. Comput. Sci.

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This paper revisits the multi-agent epistemic logic presented in [10], where agents and sets of agents are replaced by abstract, intensional "names". We make three contributions. First, we study its model theory, providing adequate notions of bisimulation and frame morphisms, and use them to study the logic's expressive power and definability. Second, we show that the logic has a natural neighborhood semantics, which in turn allows to show that the axiomatization in [10] does not rely on possibly controversial introspective properties of knowledge. Finally, we extend the logic with common and distributed knowledge operators, and provide a sound and complete axiomatization for each of these extensions. These results together put the original epistemic logic with names in a more modern context and opens the door for a logical analysis of epistemic phenomena where group membership is uncertain or variable.In [10], Grove and Halpern studied a generalized version of multi-agents epistemic logic where the usual labels for agents and sets of agents are replaced by abstract names whose extension might vary from state to state. 1 Despite being interpreted in standard multi-agents epistemic models, the resulting language does away with the familiar K i modalities, and instead contains two families of epistemic operators: S n , standing for "someone with name n knows", and E n , standing for "everyone with name n knows". This generalization is conceptually important. The "names" that index the S n and the E n modalities can refer intensionally to both individuals and groups. Since these extensions are not fixed in a given model, the logic allows to study social-epistemic phenomena that involve uncertainty or variability in the agents' identities or group membership. These phenomena are pervasive. [19,10] already provide convincing examples for distributed systems. Massive coordinated actions or social movements, especially online, also provide contemporary cases [1,4], where for instance we refer to group labels like "Trump supporters" or "trolls" without knowing exactly who the members of these groups are or even failing to know whether we, ourselves, are members of those groups. 2 The study in [10], however, focuses on the two modalities mentioned above, and in particular leaves aside notions of common and distributed knowledge. These notions are, however, central to theories of social conventions [16,2] and collective action [25].[19] study a closely related notion of common knowledge, to which we come back briefly in Section 4, but do not provide an axiomatization. Distributed knowledge for intensional or indexical group names has been studied in [20], but in a more expressive language with explicit quantification.

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Section: Morphisms and Bisimulationsmentioning

confidence: 99%

Section: Neighborhood Semanticsmentioning

confidence: 99%

“…The first part is standard, and proceeds by induction on the complexity of the formula ϕ. For the second part, the proof follows the argument in [22].…”

Section: Lemma 2 Assume B Is a Bisimulation Between A Model M And A M...mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Revisiting Epistemic Logic with Names

Bílková

Christoff

Roy

2021

Electron. Proc. Theor. Comput. Sci.

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Verifying Implicitly Quantified Modal Logic over Dynamic Networks of Processes

Padmanabha

Ramanujam

2019

Distributed Computing and Internet Technology

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Propositional Modal Logic with Implicit Modal Quantification

Padmanabha

Ramanujam

2019

Logic and Its Applications

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Propositional term modal logic is interpreted over Kripke structures with unboundedly many accessibility relations and hence the syntax admits variables indexing modalities and quantification over them. This logic is undecidable, and we consider a variable-free propositional bi-modal logic with implicit quantification. Thus [∀]α asserts necessity over all accessibility relations and [∃]α is classical necessity over some accessibility relation. The logic is associated with a natural bisimulation relation over models and we show that the logic is exactly the bisimulation invariant fragment of a two sorted first order logic. The logic is easily seen to be decidable and admits a complete axiomatization of valid formulas. Moreover the decision procedure extends naturally to the 'bundled fragment' of full term modal logic.

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Propositional Modal Logic with Implicit Modal Quantification

Cited by 8 publications

References 21 publications

Revisiting Epistemic Logic with Names

Revisiting Epistemic Logic with Names

Verifying Implicitly Quantified Modal Logic over Dynamic Networks of Processes

Propositional Modal Logic with Implicit Modal Quantification

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