2 Search Results for "Saville, Philip"

Document

DOI: 10.4230/LIPIcs.FSCD.2024.14

Two-Dimensional Kripke Semantics I: Presheaves

Authors: G. A. Kavvos

Published in: LIPIcs, Volume 299, 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)

Abstract

The study of modal logic has witnessed tremendous development following the introduction of Kripke semantics. However, recent developments in programming languages and type theory have led to a second way of studying modalities, namely through their categorical semantics. We show how the two correspond.

Cite as

G. A. Kavvos. Two-Dimensional Kripke Semantics I: Presheaves. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 14:1-14:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{kavvos:LIPIcs.FSCD.2024.14,
  author =	{Kavvos, G. A.},
  title =	{{Two-Dimensional Kripke Semantics I: Presheaves}},
  booktitle =	{9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  pages =	{14:1--14:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-323-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{299},
  editor =	{Rehof, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2024.14},
  URN =		{urn:nbn:de:0030-drops-203438},
  doi =		{10.4230/LIPIcs.FSCD.2024.14},
  annote =	{Keywords: modal logic, categorical semantics, Kripke semantics, duality, open maps}
}

Document

DOI: 10.4230/LIPIcs.FSCD.2017.16

List Objects with Algebraic Structure

Authors: Marcelo Fiore and Philip Saville

Published in: LIPIcs, Volume 84, 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)

Abstract

We introduce and study the notion of list object with algebraic structure. The first key aspect of our development is that the notion of list object is considered in the context of monoidal structure; the second key aspect is that we further equip list objects with algebraic structure in this setting. Within our framework, we observe that list objects give rise to free monoids and moreover show that this remains so in the presence of algebraic structure. In addition, we provide a basic theory explicitly describing as an inductively defined object such free monoids with suitably compatible algebraic structure in common practical situations. This theory is accompanied by the study of two technical themes that, besides being of interest in their own right, are important for establishing applications. These themes are: parametrised initiality, central to the universal property defining list objects; and approaches to algebraic structure, in particular in the context of monoidal theories. The latter leads naturally to a notion of nsr (or near semiring) category of independent interest. With the theoretical development in place, we touch upon a variety of applications, considering Natural Numbers Objects in domain theory, giving a universal property for the monadic list transformer, providing free instances of algebraic extensions of the Haskell Monad type class, elucidating the algebraic character of the construction of opetopes in higher-dimensional algebra, and considering free models of second-order algebraic theories.

Cite as

Marcelo Fiore and Philip Saville. List Objects with Algebraic Structure. In 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 84, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

Copy BibTex To Clipboard

@InProceedings{fiore_et_al:LIPIcs.FSCD.2017.16,
  author =	{Fiore, Marcelo and Saville, Philip},
  title =	{{List Objects with Algebraic Structure}},
  booktitle =	{2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)},
  pages =	{16:1--16:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-047-7},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{84},
  editor =	{Miller, Dale},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2017.16},
  URN =		{urn:nbn:de:0030-drops-77262},
  doi =		{10.4230/LIPIcs.FSCD.2017.16},
  annote =	{Keywords: list object, free monoid, strong monad, (cartesian, linear, and second-order) algebraic theory, near semiring, Haskell Monad type class, opetope}
}

Refine by Author
1 Fiore, Marcelo
1 Kavvos, G. A.
1 Saville, Philip

Refine by Classification
1 Theory of computation → Categorical semantics
1 Theory of computation → Modal and temporal logics

Refine by Keyword
1 (cartesian
1 Haskell Monad type class
1 Kripke semantics
1 and second-order) algebraic theory
1 categorical semantics
Show More...

Refine by Type
2 document

Refine by Publication Year
1 2017
1 2024