An Invitation to New Essays on Belnap-Dunn Logic

Omori, Hitoshi; Wansing, Heinrich

doi:10.1007/978-3-030-31136-0_1

Cited by 6 publications

(17 citation statements)

References 30 publications

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“…Mutliferroics, the systems with interacting magnetic and electric degrees of freedom, broaden the scope of the existing current hardware concepts 7,[37][38][39][40][41][42][43][44][45][46][47][48][49] and introduce the new ones, see [50][51][52][53] . Magnetic mutliferroic tunnel junctions promise the platform for the computers based on the non-binary (many-valued) logics 54 .…”

Section: Discussionmentioning

confidence: 99%

Time-dependent exchange creates the time-frustrated state of matter

Valiulin

Chtchelkatchev

Mikheyenkov

et al. 2022

Sci Rep

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Magnetic systems governed by exchange interactions between magnetic moments harbor frustration that leads to ground state degeneracy and results in the new topological state often referred to as a frustrated state of matter (FSM). The frustration in the commonly discussed magnetic systems has a spatial origin. Here we demonstrate that an array of nanomagnets coupled by the real retarded exchange interactions develops a new state of matter, time frustrated matter (TFM). In a spin system with the time-dependent retarded exchange interaction, a single spin-flip influences other spins not instantly but after some delay. This implies that the sign of the exchange interaction changes, leading to either ferro- or antiferromagnetic interaction, depends on time. As a result, the system’s temporal evolution is essentially non-Markovian. The emerging competition between different magnetic orders leads to a new kind of time-core frustration. To establish this paradigmatic shift, we focus on the exemplary system, a granular multiferroic, where the exchange transferring medium has a pronounced frequency dispersion and hence develops the TFM.

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Section: Discussionmentioning

confidence: 99%

Time-dependent exchange creates the time-frustrated state of matter

Valiulin

Chtchelkatchev

Mikheyenkov

et al. 2022

Sci Rep

View full text Add to dashboard Cite

show abstract

“…Mutliferroics, the systems with interacting magnetic and electric degrees of freedom, broaden the scope of the existing current hardware concepts 7,[44][45][46][47][48][49][50][51][52][53][54][55][56] and introduce the new ones, see [57][58][59][60] . Magnetic mutliferroic tunnel junctions promise the platform for the computers based on the non-binary (many-valued) logics 61 .…”

Section: Discussionmentioning

confidence: 99%

Time-dependent exchange creates the time-frustrated state of matter

Valiulin,

Chtchelkatchev,

Mikheyenkov

et al. 2022

Preprint

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Magnetic systems governed by exchange interactions between magnetic moments harbor frustration that leads to ground state degeneracy and results in the new topological state often referred to as a frustrated state of matter (FSM). The frustration in the commonly discussed magnetic systems has a spatial origin. Here we demonstrate that an array of nanomagnets coupled by the real retarded exchange interactions develops a new state of matter, time frustrated matter (TFM). In a spin system with the time-dependent retarded exchange interaction, a single spin-flip influences other spins not instantly but after some delay. This implies that the sign of the exchange interaction changes, leading to either ferro-or antiferromagnetic interaction, depends on time. As a result, the system's temporal evolution is essentially non-Markovian. The emerging competition between different magnetic orders leads to a new kind of time-core frustration. To establish this paradigmatic shift, we focus on the exemplary system, a granular multiferroic, where the exchange transferring medium has a pronounced frequency dispersion and hence develops the TFM.

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“…Since contraposition is an admissible rule in FDE, two formulas ∼A and ∼B are mutually derivable in a proof system for FDE if A and B are mutually derivable, and, as a result, ∼ is not congruentiality-breaking in FDE. The bilateral natural deduction proof systems in [36] for FDE and variants of FDE for which contraposition is an admissible rule are, however, well motivated already, though less strongly, by the purity of their introduction and elimination rules in comparison to the impurity of their unilateral counterparts.…”

Section: Definition 10mentioning

confidence: 99%

Logical Multilateralism

Wansing,

Ayhan

2023

J Philos Logic

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In this paper we will consider the existing notions of bilateralism in the context of proof-theoretic semantics and propose, based on our understanding of bilateralism, an extension to logical multilateralism. This approach differs from what has been proposed under this name before in that we do not consider multiple speech acts as the core of such a theory but rather multiple consequence relations. We will argue that for this aim the most beneficial proof-theoretical realization is to use sequent calculi with multiple sequent arrows satisfying some specific conditions, which we will lay out in this paper. We will unfold our ideas with the help of a case study in logical tetralateralism and present an extension of Almukdad and Nelson’s propositional constructive four-valued logic by unary operations of meaningfulness and nonsensicality. We will argue that in sequent calculi with multiple sequent arrows it is possible to maintain certain features that are desirable if we assume an understanding of the meaning of connectives in the spirit of proof-theoretic semantics. The use of multiple sequent arrows will be justified by the presence of congruentiality-breaking unary connectives.

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An Invitation to New Essays on Belnap-Dunn Logic

Cited by 6 publications

References 30 publications

Time-dependent exchange creates the time-frustrated state of matter

Time-dependent exchange creates the time-frustrated state of matter

Time-dependent exchange creates the time-frustrated state of matter

Logical Multilateralism

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