The Monodic Fragment of Propositional Term Modal Logic

Padmanabha, Anantha; Ramanujam, R.

doi:10.1007/s11225-018-9784-x

Cited by 15 publications

(19 citation statements)

References 15 publications

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“…Also, ϕ is valid if ¬ϕ is not satisfiable. In [18], we prove that the satisfiability problem for PTML is undecidable.…”

Section: The Logicmentioning

confidence: 99%

“…However, when we come to PTML, since the agent set is not fixed, we need to have the notion of 'world bisimilarity' as well as 'agent bisimilarity'. Towards this, in [18], we introduce a notion of bisimulation for propositional term modal logic and show that it preserves PTML formulas.…”

Section: Iqml Bisimulation and Elementary Equivalencementioning

confidence: 99%

“…Hence the question of finding decidable fragments of PTML is well motivated. In [18] we prove that the monodic fragment of PTML is decidable. The monodic fragment is a restriction allowing at most one free variable within the scope of a modality.…”

Section: Introductionmentioning

confidence: 99%

“…Note that TML extends first order logic, and hence its satisfiability problem is undecidable. In [18] we prove that the problem is undecidable even when the atoms are restricted to boolean propositions (PTML). Hence the question of finding decidable fragments of PTML is well motivated.…”

Section: Introductionmentioning

confidence: 99%

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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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“…Also, ϕ is valid if ¬ϕ is not satisfiable. In [18], we prove that the satisfiability problem for PTML is undecidable.…”

Section: The Logicmentioning

confidence: 99%

Section: Iqml Bisimulation and Elementary Equivalencementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Propositional Modal Logic with Implicit Modal Quantification

Padmanabha

Ramanujam

2019

Logic and Its Applications

Self Cite

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“…Full first-order term modal language is clearly undecidable. In [16], it is shown that even its propositional fragment is undecidable, 2 and the addition of the program modalities in dynamic logic makes things worse. As Kooi remarks in [13], the combination of term modal logic and dynamic assignment logic is not even recursively enumerable.…”

Section: Introductionmentioning

confidence: 99%

When Names Are Not Commonly Known: Epistemic Logic with Assignments

Wang,

Seligman

2018

Preprint

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In standard epistemic logic, agent names are usually assumed to be common knowledge implicitly. This is unreasonable for various applications. Inspired by term modal logic and assignment operators in dynamic logic, we introduce a lightweight modal predicate logic where names can be non-rigid. The language can handle various de dicto /de re distinctions in a natural way. The main technical result is a complete axiomatisation of this logic over S5 models.

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Formalizing rough sets using a new noncontingency axiomatic system

Deng

Guan

Wang

et al. 2021

Int J of Intelligent Sys

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Formalization of rough sets is a key issue in rough set theory. When rough sets are formalized by propositional logic, predicate logic, or modal propositional logic, it easily suffers from some problems. For instance, an incomplete system is obtained. The concepts of “ p r e c i s e” or “ r o u g h” of rough sets cannot be described. To tackle these issues, a new noncontingency axiomatic system is proposed for formalizing rough sets in this paper. First, a new concise accessibility relation is defined for the axiomatic system; then, two simpler axiom schemas of the axiomatic system are designed to replace the axiom schema K. This is helpful to prove the soundness and completeness theorems for the axiomatic system. Finally, rough sets can be perfectly formalized by our proposed axiomatic system. Theoretical analysis proves that a complete formal system is achieved. In addition, the concepts of “ p r e c i s e” or “ r o u g h” of rough sets can be described without the help of semantics functions of metalanguage.

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The Monodic Fragment of Propositional Term Modal Logic

Cited by 15 publications

References 15 publications

Propositional Modal Logic with Implicit Modal Quantification

Propositional Modal Logic with Implicit Modal Quantification

When Names Are Not Commonly Known: Epistemic Logic with Assignments

Formalizing rough sets using a new noncontingency axiomatic system

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