Bundled Fragments of First-Order Modal Logic: (Un)Decidability

Padmanabha, Anantha; Ramanujam, R.; Wang, Yanjing

doi:10.4230/lipics.fsttcs.2018.43

Cited by 9 publications

(14 citation statements)

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“…Inspired by Hinttika's early idea and discussions in philosophy and linguistics about embedded wh-questions [12,28], Wang proposed to introduce the bundle modalities that pack a quantifier and an epistemic modality together to capture each know-wh as a whole, instead of breaking it down into smaller components [30]. This leads to a new family of (non-normal) epistemic logics of know-wh and new decidable fragments of first-order modal logics [29,23]. Now a very natural question arises, how do we capture the dynamics of such de re knowledge?…”

Section: De Re Knowledge and Updatesmentioning

confidence: 99%

De Re Updates

Cohen

Tang

Wang

2021

Electron. Proc. Theor. Comput. Sci.

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In this paper, we propose a lightweight yet powerful dynamic epistemic logic that captures not only the distinction between de dicto and de re knowledge but also the distinction between de dicto and de re updates. The logic is based on the dynamified version of an epistemic language extended with the assignment operator borrowed from dynamic logic, following the work of Wang and Seligman [35]. We obtain complete axiomatizations for the counterparts of public announcement logic and event-model-based DEL based on new reduction axioms taking care of the interactions between dynamics and assignments.

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Section: De Re Knowledge and Updatesmentioning

confidence: 99%

De Re Updates

Cohen

Tang

Wang

2021

Electron. Proc. Theor. Comput. Sci.

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“…Encouraged by this, [14] took the next step, by considering not only the combination ∃x but also its companion ∀x . They found that the logic with both of these combinations continued to be decidable over increasing domain models, though it was later shown that there was a price to be paid in terms of complexity.…”

Section: Introductionmentioning

confidence: 99%

“…∃x (∃y (x > y) ∧ ∃y (x < y)): There is an element that dominates another no matter the update and is dominated by another no matter the update. The story in [14] came with a twist: the computational property of many bundled fragments depends on whether you assume the domain of each world is constant or only expanding along the relation. 1 In the former, a single domain is fixed for the entire model, with only predicate interpretations changing during system evolution.…”

Section: Introductionmentioning

confidence: 99%

“…This is natural in the context of systems of processes where new sub-processes are created during system evolution, and in security theory, where new parallel sessions of security protocols are spawned. [14] showed that while the ∃x bundle cannot distinguish between the two interpretations, even the fragment of ∀ with only unary predicates is undecidable over constant domain models. For other decidable fragments such as the monodic fragment, there is a natural translation showing that for any formula over a varying domain model, there is an equisatisfiable formula over a constant domain model.…”

Section: Introductionmentioning

confidence: 99%

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Are Bundles Good Deals for FOML?

Liu¹,

Padmanabha²,

Ramanujam³

et al. 2022

Preprint

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Bundled products are often offered as good deals to customers. When we bundle quantifiers and modalities together (as in ∃x , ♦∀x etc.) in first-order modal logic (FOML), we get new logical operators whose combinations produce interesting fragments of FOML without any restriction on the arity of predicates, the number of variables, or the modal scope. It is well-known that finding decidable fragments of FOML is hard, so we may ask: do bundled fragments that exploit the distinct expressivity of FOML constitute good deals in balancing the expressivity and complexity? There are a few positive earlier results on some particular fragments. In this paper, we try to fully map the terrain of bundled fragments of FOML in (un)decidability, and in the cases without a definite answer yet, we show that they lack the finite model property. Moreover, whether the logics are interpreted over constant domains (across states/worlds) or increasing domains presents another layer of complexity. We also present the loosely bundled fragment, which generalizes the bundles and yet retain decidability (over increasing domain models).

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“…Standard Epistemic Logic (EL) mainly studies reasoning patterns of knowing that ϕ, despite early contributions by Hintikka on formulating other know-wh expressions such as knowing who and why using first-order and higher-order modal logic. In recent years, there is a resurgence of interest on epistemic logics of know-wh powered by the new techniques for fragments of firstorder modal logic based on the so-called bundle modalities packing a quantifier and a normal epistemic modality together [26,24,21]. Within the varieties of logics of know-wh, the logics of know-how received the most attention in AI (cf.…”

Section: Introductionmentioning

confidence: 99%

Knowing How to Plan

Yan-jun

Wang

2021

Electron. Proc. Theor. Comput. Sci.

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Various planning-based know-how logics have been studied in the recent literature. In this paper, we use such a logic to do know-how-based planning via model checking. In particular, we can handle the higher-order epistemic planning involving know-how formulas as the goal, e.g., find a plan to make sure p such that the adversary does not know how to make p false in the future. We give a PTIME algorithm for the model checking problem over finite epistemic transition systems and axiomatize the logic under the assumption of perfect recall. * Corresponding author. Yanjing Wang thanks the support of NSSF grant 19BZX135.

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Bundled Fragments of First-Order Modal Logic: (Un)Decidability

Cited by 9 publications

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Are Bundles Good Deals for FOML?

Knowing How to Plan

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