Whitehead all shared Leibniz's dream of combining symbolic logic , mathematics , and philosophy. According to Helena Rasiowa , "The years saw, in particular in the Polish school of logic, researches on non-classical propositional calculi conducted by what is termed the logical matrix method.

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Since logical matrices are certain abstract algebras, this led to the use of an algebraic method in logic. Brady discusses the rich historical connections between algebraic logic and model theory. Alfred Tarski , the founder of set theoretic model theory as a major branch of contemporary mathematical logic, also:. In the practice of the calculus of relations, Jacques Riguet used the algebraic logic to advance useful concepts: he extended the concept of an equivalence relation on a set to heterogeneous relations with the difunctional concept.

Riguet also extended ordering to the heterogeneous context by his note that a staircase logical matrix has a complement that is also a staircase, and that the theorem of N.

Ferrers follows from interpretation of the transpose of a staircase. Riguet generated rectangular relations by taking the outer product of logical vectors; these contribute to the non-enlargeable rectangles of formal concept analysis. Leibniz had no influence on the rise of algebraic logic because his logical writings were little studied before the Parkinson and Loemker translations.

Our present understanding of Leibniz as a logician stems mainly from the work of Wolfgang Lenzen, summarized in Lenzen To see how present-day work in logic and metaphysics can draw inspiration from, and shed light on, Leibniz's thought, see Zalta From Wikipedia, the free encyclopedia. Categories : Algebraic logic History of logic. Hidden categories: Commons category link from Wikidata. Namespaces Article Talk.

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Scanned copy freely available. Some theorems on structural consequence operations.

Studia Logica 34 , 1—9. A Course in Universal Algebra. The Millenium Edition. Electronic version freely available. First edition published as vol. On elementary equivalence for equality-free logic.

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Notre Dame Journal of Formal Logic 37 , — Model Theory , 3rd ed. North-Holland, Amsterdam, Reprinted by Dover Publications, New York, Protoalgebraic logics , vol. Kluwer Academic Publishers, Dordrecht, Mathematical logic , second ed. Undergraduate Texts in Mathematics. Springer-Verlag, New York, A mathematical introduction to logic , 2nd ed. Academic Press, New York, Belnap's four-valued logic and De Morgan lattices. Abstract algebraic logic - an introductory chapter.

## Logic, Algebra and Truth Degrees 2014

Galatos and K. I will first give a short introduction in logic and, in particular, in the use of duality theory in logic. Thereafter we turn to classical first order logic. I will explain what these are by abstracting the essential properties of the collection of all first order formulas over a given signature. Thereafter we may identify the dual notion of a Boolean hyperdoctrine and consequently describe a duality for CFOL. June 8: Sam van Gool , Canonical extensions and Stone duality for strong proximity lattices.

Stably compact spaces are topological spaces which were proposed as the generalisation of compact Hausdorff spaces to the T0 setting. Since distributive lattices are in the famous Stone duality [3] with spectral spaces, it is natural to wonder what additional structure on spectral spaces corresponds to the relation of a strong proximity lattice.

We show that, up to isomorphism, strong proximity lattices correspond to spectral spaces with a retraction, and that the image of this retraction is precisely the stably compact space which the strong proximity lattice represents. In particular, we use this duality to retrieve the result from Johnstone [1] that stably compact spaces are precisely the retracts of spectral spaces.

Johnstone , Stone spaces , Cambridge studies in advanced mathematics, vol. Andima , R. Flagg, G. Itzkowitz , P. Misra , Y. Kong, and R. Kopperman , eds. Stone, Topological representation of distributive lattices and brouwerian logics, Casopis pro pestovani matematiky a fysiky 67 , April HG Ronald Meester aan de Vrije Universiteit Amsterdam. One of the simplifying assumptions in this model is uniform mixing between the individuals, which means that all individuals meet each other at equal rate. We introduce two extended models, the Hierarchical and Random model, where every individual i.

So these social networks overlap and the rate of disease transmission between two individuals depends on the subgroup they both belong to. The two models are different in the way how the social levels of households and schools are interlinked. In the Hierarchical model, all children in each household go to the same school, while in the Random model every household member goes independently of his or her sibling to a randomly chosen school.

Additionally, in both models we assume that all individuals are equally likely to meet each other outside of their households and schools, called the community. To compute the threshold parameter and expected final epidemic size of these models heuristically, we have observed the spread of the disease in a slightly different way where the time dynamics are left out of consideration , such that we could use branching approximations.

These approximate results are shown to be exact as the population size tends to infinity. We have compared both models on their main characteristics heuristically by proving that in the start of the epidemic, the Hierarchical model is stochastically dominated by the Random model. January HG Voor het eerst goed beschreven door Robinson Het zal blijken dat de constructie van dit lichaam niet uniek is en verschillende lichamen oplevert. Echter , onder enkele sterke aannames , kunnen we laten zien dat deze lichamen isomorf met elkaar zijn.

Dit laatste kunnen we bewijzen door een resultaat te gebruiken uit een artikel van Erdoes , Gillman en Henriksen Effect algebras are latest in a line of structures aiming to model quantum logic. Effect algebras are algebraic structures with a partially defined addition.

## Applied Optics

The key example are all positive self- adjoint linear maps on a Hilbert space below the identity. We'll take a categorical look at effect algebras. In particular we'll construct an adjunction between Boolean algebras and effect algebras. December Michael Naehrig , Pairings for cryptography. All are welcome!

## The Algebra of Logic Tradition (Stanford Encyclopedia of Philosophy)

December 2: Jonas Frey , Universite Paris 7, A universal characterization of the tripos-to-topos construction. Abstract: The concept of elementary topos was introduced by Lawvere and Tierney around as a generalization of Grothendieck's notion of topos nowadays known as Grothendieck topos , motivated by logical and foundational questions. Finally, in , Hyland, Johnstone and Pitts described a construction which gives rise to toposes other than Grothendieck toposes.

This construction starts from " triposes ", which are certain fibrations used in categorical logic. The most prominent topos that can be obtained in this way is the "effective topos ", which was described in an article by Hyland in I will begin my talk by giving a detailed and elementary description of the effective topos , using a decomposition of Hyland's original construction in two steps. Then I will define the general concept of " tripos ", and explain how the decomposition of the construction which was demonstrated at the example of the effective topos allows us to give a characterization of the tripos-to-topos construction as a kind of biadjunction between a 2-category of triposes and a 2-category of toposes.

See abstract. The former uses the canonical extension of the original lattice and it is in fact a skeleton of the canonical extension. The later is based directly on the original lattice using topology, but if we drop the topology, the resulting structure is equivalent to the RS-frame of the canonical extension of the original lattice. The method of toggling between these two frameworks is made explicit and then we proceed to expand it to an additional operation in this case, a negation , based on earlier work on dualities for lattices with negation via Urquhart duality by W. Dzik , E.

This correspondence enabled us to sort out a problem posed by the former authors in their paper. Abstract: See pdf. Abstract: Inquisitive semantics is a tool which allows us to represent the inquisitive content of a formula as well as the informative one. I will first introduce the system and explain some of its basic properties. Finally, Inquisitive logic will be presented as the limit of a hierarchy of logics arising by imposing restrictions on the semantics. Abstract: co-authors: Mai Gehrke, Serge Grigorieff I will present a survey of the equational theory of regular languages.