Relevant bibliographies by topics / Adjoint modalities

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Academic literature on the topic 'Adjoint modalities'

Author: Grafiati
Published: 2 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Adjoint modalities"

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Gratzer, Daniel, Evan Cavallo, G. A. Kavvos, Adrien Guatto, and Lars Birkedal. "Modalities and Parametric Adjoints." ACM Transactions on Computational Logic 23, no. 3 (2022): 1–29. http://dx.doi.org/10.1145/3514241.

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Birkedal et al. recently introduced dependent right adjoints as an important class of (non-fibered) modalities in type theory. We observe that several aspects of their calculus are left underdeveloped and that it cannot serve as an internal language. We resolve these problems by assuming that the modal context operator is a parametric right adjoint. We show that this hitherto unrecognized structure is common. Based on these discoveries we present a new well-behaved Fitch-style multimodal type theory, which can be used as an internal language. Finally, we apply this syntax to guarded recursion
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BÍLKOVÁ, MARTA, JIŘÍ VELEBIL, and YDE VENEMA. "On monotone modalities and adjointness." Mathematical Structures in Computer Science 21, no. 2 (2011): 383–416. http://dx.doi.org/10.1017/s0960129510000514.

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We fix a logical connection (Stone ˧ Pred : Setop → BA given by 2 as a schizophrenic object) and study coalgebraic modal logic that is induced by a functor T: Set → Set that is finitary and standard and preserves weak pullbacks and finite sets. We prove that for any such T, the cover modality nabla is a left (and its dual delta is a right) adjoint relative to ω. We then consider monotone unary modalities arising from the logical connection and show that they all are left (or right) adjoints relative to ω.
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SADRZADEH, MEHRNOOSH, and ROY DYCKHOFF. "POSITIVE LOGIC WITH ADJOINT MODALITIES: PROOF THEORY, SEMANTICS, AND REASONING ABOUT INFORMATION." Review of Symbolic Logic 3, no. 3 (2010): 351–73. http://dx.doi.org/10.1017/s1755020310000134.

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We consider a simple modal logic whose nonmodal part has conjunction and disjunction as connectives and whose modalities come in adjoint pairs, but are not in general closure operators. Despite absence of negation and implication, and of axioms corresponding to the characteristic axioms of (e.g.) T, S4, and S5, such logics are useful, as shown in previous work by Baltag, Coecke, and the first author, for encoding and reasoning about information and misinformation in multiagent systems. For the propositional-only fragment of such a dynamic epistemic logic, we present an algebraic semantics, usi
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Sadrzadeh, Mehrnoosh, and Roy Dyckhoff. "Positive Logic with Adjoint Modalities: Proof Theory, Semantics and Reasoning about Information." Electronic Notes in Theoretical Computer Science 249 (August 2009): 451–70. http://dx.doi.org/10.1016/j.entcs.2009.07.102.

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SHULMAN, MICHAEL. "Brouwer's fixed-point theorem in real-cohesive homotopy type theory." Mathematical Structures in Computer Science 28, no. 6 (2017): 856–941. http://dx.doi.org/10.1017/s0960129517000147.

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We combine homotopy type theory with axiomatic cohesion, expressing the latter internally with a version of ‘adjoint logic’ in which the discretization and codiscretization modalities are characterized using a judgemental formalism of ‘crisp variables.’ This yields type theories that we call ‘spatial’ and ‘cohesive,’ in which the types can be viewed as having independent topological and homotopical structure. These type theories can then be used to study formally the process by which topology gives rise to homotopy theory (the ‘fundamental ∞-groupoid’ or ‘shape’), disentangling the ‘identifica
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Ali, Arsalan Akbar, Benjamin Matthew Jacobs, Artee Gandhi, and Meredith Brooks. "Baastrup’s Disease in Pediatric Gymnasts." Children 9, no. 7 (2022): 1018. http://dx.doi.org/10.3390/children9071018.

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Baastrup’s disease is a rare, often misdiagnosed, and causes back pain in children. It is characterized by degenerative changes of both spinous processes and interspinous soft tissues between two adjacent vertebrae. Repetitive spinal movements in the sagittal plane predispose injury to posterior elements of the spine. Chronic flexion and extension strain the interspinous ligament, causing the neighboring spinous processes to adjoin. Patients typically report midline back pain in the lumbar region, which radiates both cephalad and caudad but not laterally. Pain is aggravated by extension and pa
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Shulman, Michael. "Semantics of multimodal adjoint type theory." Electronic Notes in Theoretical Informatics and Computer Science Volume 3 - Proceedings of... (November 23, 2023). http://dx.doi.org/10.46298/entics.12300.

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We show that contrary to appearances, Multimodal Type Theory (MTT) over a 2-category M can be interpreted in any M-shaped diagram of categories having, and functors preserving, M-sized limits, without the need for extra left adjoints. This is achieved by a construction called "co-dextrification" that co-freely adds left adjoints to any such diagram, which can then be used to interpret the "context lock" functors of MTT. Furthermore, if any of the functors in the diagram have right adjoints, these can also be internalized in type theory as negative modalities in the style of FitchTT. We introdu
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Denolle, Marine A., Carl Tape, Ebru Bozdağ, et al. "Training the Next Generation of Seismologists: Delivering Research-Grade Software Education for Cloud and HPC Computing Through Diverse Training Modalities." Seismological Research Letters, June 5, 2025. https://doi.org/10.1785/0220240413.

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Abstract With the rise of data volume and computing power, seismological research requires more advanced skills in data processing, numerical methods, and parallel computing. We present the experience of conducting training workshops in various forms of delivery to support the adoption of large-scale high-performance computing (HPC) and cloud computing, advancing seismological research. The seismological foci were on earthquake source parameter estimation in catalogs, forward and adjoint wavefield simulations in 2D and 3D at local, regional, and global scales, earthquake dynamics, ambient nois
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Emmerson, Parker. "Anterolateral Lite 2." Journal of Liberated Mathematics, May 25, 2025. https://doi.org/10.5281/zenodo.15510371.

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The \emph{Anterolateral Lite 2} formalism arises from a need to robustly track analytic and symbolic distinctions that are often lost in traditional algebraic and geometric frameworks, especially in contexts involving multi-branched solutions and subtle phase phenomena, such as Lorentzian and radical expressions. Classical algebraic structures, which treat coordinates as atomic or globally coherent entities, are prone to \emph{branch collapse}: the unwanted identification of distinct solution branches through singularities, degenerate loci, or insufficiently expressive type systems. Building o
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Dagnino, Francesco, and Giuseppe Rosolini. "Doctrines, modalities and comonads." Mathematical Structures in Computer Science, September 14, 2021, 1–30. http://dx.doi.org/10.1017/s0960129521000207.

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Abstract Doctrines are categorical structures very apt to study logics of different nature within a unified environment: the 2-category Dtn of doctrines. Modal interior operators are characterised as particular adjoints in the 2-category Dtn. We show that they can be constructed from comonads in Dtn as well as from adjunctions in it, and we compare the two constructions. Finally we show the amount of information lost in the passage from a comonad, or from an adjunction, to the modal interior operator. The basis for the present work is provided by some seminal work of John Power.
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Book chapters on the topic "Adjoint modalities"

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Lakhani, Zeeshan, Ankush Das, Henry DeYoung, Andreia Mordido, and Frank Pfenning. "Polarized Subtyping." In Programming Languages and Systems. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-99336-8_16.

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AbstractPolarization of types in call-by-push-value naturally leads to the separation of inductively defined observable values (classified by positive types), and coinductively defined computations (classified by negative types), with adjoint modalities mediating between them. Taking this separation as a starting point, we develop a semantic characterization of typing with step indexing to capture observation depth of recursive computations. This semantics justifies a rich set of subtyping rules for an equirecursive variant of call-by-push-value, including variant and lazy records. We further
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Conference papers on the topic "Adjoint modalities"

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Li, Kang, Xiaoping Qian, and Alejandro A. Espinoza Orías. "Efficient Construction of Statistical Shape Models for Patient-Specific Modeling." In ASME 2013 Conference on Frontiers in Medical Devices: Applications of Computer Modeling and Simulation. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/fmd2013-16113.

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Statistical Shape Modeling (SSM) is a powerful tool to capture the shape variation pattern across a group of shapes belonging to a certain shape class. SSM has seen many promising applications for the purpose of building Patient-Specific Model (PSM) because it avoids unwanted exposure to ionizing radiation from imaging modalities such as CT scanning and has potential as a cost-saving and time-efficient research and clinical tool. All that is needed to reconstruct the patient — specific data is to instantiate the statistical model already generated. The utility of the statistical model relies o
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