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Polyadic Quantification via Denoting Concepts

Ori Simchen
2010 Notre Dame Journal of Formal Logic  
The question of the origin of polyadic expressivity is explored and the results are brought to bear on Bertrand Russell's 1903 theory of denoting concepts, which is the main object of criticism in his  ...  It is shown that, appearances to the contrary notwithstanding, the background ontology of the earlier theory of denoting enables the full-blown expressive power of first-order polyadic quantification theory  ...  The theory of denoting concepts is thus vindicated, offering the full expressivity of first-order polyadic quantification theory without variable-binding.  ... 
doi:10.1215/00294527-2010-023 fatcat:vkzm5lp3hzcv3eroeckmbq2i6a

The Syntax of the World

W. D. Hart
1996 Crítica. Revista Hispanoamericana de Filosofía  
. , X ip ) is a quantificational relation, then so is its complement with respect to X; its polyadicity is that of Q.  ...  We might take these sentences as applying the complex predicates F xy ∨ F yz (∀x) F yx to, respectively, the triple of the denotations of 'a', 'b', 'c', and the denotation of 'a'.  ... 
doi:10.22201/iifs.18704905e.1996.1032 fatcat:y6eww67wfre2boik7ioywl7doi

Description logics as polyadic modal logics [article]

Jonne Iso-Tuisku, Antti Kuusisto
2021 arXiv   pre-print
We promote a natural approach to such logics via general relation algebras that can be used to define operations on relations of all arities.  ...  We study extensions of standard description logics to the framework of polyadic modal logic.  ...  Indeed, the approach via polyadic modal logic is only one of many related possibilities.  ... 
arXiv:2108.08838v1 fatcat:fxknqnzh4nb3bnx7lt7nhctdmy

Computational complexity of polyadic lifts of generalized quantifiers in natural language

Jakub Szymanik
2010 Linguistics and Philosophy  
We study the computational complexity of polyadic quantifiers in natural language. This type of quantification is widely used in formal semantics to model the meaning of multi-quantifier sentences.  ...  Keywords: generalized quantifier theory; computational complexity; polyadic quantification; multiquantifier sentences; Strong Meaning Hypothesis Introduction Quantifier expressions occur whenever we describe  ...  Moreover, we will need a concept of relativization defined via oracle machines.  ... 
doi:10.1007/s10988-010-9076-z fatcat:ijq5n2sucvgttgemw67qhuug44

The Basic Concepts of Algebraic Logic

Paul R. Halmos
1956 The American mathematical monthly  
A polyadic logic is a pair (A, M), where A is a polyadic algebra and M is a polyadic ideal in 1956] THE BASIC CONCEPTS OF ALGEBRAIC LOGIC 383 A.  ...  What should be mentioned, how- ever, is that there is another way of algebraizing the functional calculus with equality, namely, via Tarski’s concept of a cylindric algebra.  ... 
doi:10.1080/00029890.1956.11988821 fatcat:vnajavyvavek3n4bk6affn7eue

Directions in generalized quantifier theory

Johan van Benthem, Dag Westerståhl
1995 Studia Logica: An International Journal for Symbolic Logic  
A systematic study of such polyadic patterns would thus be quite interesting. First, what are most general schemas of definition for polyadic quantification (cf. Sher 1991 , Spaan 1993 ?  ...  And corresponding results may be obtainable also for infinite models. 10 Polyadic quantifiers and linguistic definability The quantifiers appearing as denotations of determiners in natural languages  ... 
doi:10.1007/bf01057805 fatcat:akb4jxe4ubambnw3p5b2o2o2si

Tensor Computation: A New Framework for High-Dimensional Problems in EDA

Zheng Zhang, Kim Batselier, Haotian Liu, Luca Daniel, Ngai Wong
2017 IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems  
., nonlinear circuit modeling and high-dimensional uncertainty quantification), and suggests further open EDA problems where the use of tensor computation could be of advantage.  ...  These tensors were then decomposed via e.g.  ...  Nonetheless, tensors still seem a relatively unexplored and unexploited concept in the EDA field.  ... 
doi:10.1109/tcad.2016.2618879 fatcat:4li26hkadvex5c3xs3eb2ijwk4

Lexicalizing and Combining [chapter]

Paul M. Pietroski
2014 Cognitive Science Perspectives on Verb Representation and Processing  
from the polyadic concepts expressed with verbs.  ...  polyadic concepts saturated by the singular concepts expressed with names.  ... 
doi:10.1007/978-3-319-10112-5_2 fatcat:erbdqpbccncfnolgn6h3kczupa

Paul M. Pietroski: Conjoining Meanings. Semantics Without Truth Values

Kai-Uwe Carstensen
2019 Zeitschrift für Sprachwissenschaft  
Instead, Pietroski proposes to view meanings as instructions for how to access simple concepts or build complex concepts.  ...  The alternative he then previews is based on a restricted kind of predication (only classificatory monadic concepts of type ⟨M⟩ and relational dyadic concepts of type ⟨D⟩) with corresponding compositional  ...  Quantification is treated à la mode in CM.  ... 
doi:10.1515/zfs-2019-2005 fatcat:gkjw6wpihzeetceswwjkakgis4

The Logic of Finite Order

Simon Hewitt
2012 Notre Dame Journal of Formal Logic  
In rough outline, SL permits quantification over, and reference to, some finite number of things in an order, in an ordinary everyday sense of the word "order," and superplural quantification over things  ...  It is one thing to allow that there are such things as serial denotation and quantification.  ...  If (polyadic) second-order quantification is over tuples, then it is not ontologically innocent.  ... 
doi:10.1215/00294527-1716820 fatcat:4owuktiuvbc5pjbabdxz2af6w4

On the uniform one-dimensional fragment [article]

Antti Kuusisto
2016 arXiv   pre-print
For example the DL FU 1 -concept ¬∃(¬R).A, where R is a binary role, is satisfied in an interpretation consisting of a single element u that satisfies A and connects to itself via R.  ...  Consider a concept D of DLR 0 reg .  ... 
arXiv:1604.01673v2 fatcat:bq6bg7pqxrhynmyh2ogegsufzy

Interpolation in many valued predicate logics using algebraic logic [article]

Tarek Sayed Ahmed
2013 arXiv   pre-print
Using polyadic MV algebras, we show that many predicate many valued logics have the interpolation property.  ...  We now define an important concept in algebraic logic. This concept occurs under the rubric of neat reducts in cylindric algebras [22] , [7] and compressions in polyadic algebras [12] .  ...  This concept of dimension restricted free algebras conquers this difficulty. It is a deep concept due to Tarski that we borrow from cylindric algebras.  ... 
arXiv:1304.0760v1 fatcat:dr554ooorreqpidsujttnnbehq

On the Consistency of a Plural Theory of Frege's Grundgesetze

Francesca Boccuni
2011 Studia Logica: An International Journal for Symbolic Logic  
It exploits the notion of plural quantification and a few Fregean devices, among which the infamous Basic Law V. In this paper, a model-theoretical consistency proof for the system PG is provided.  ...  Overview The aim of the paper is to provide a model-theoretic consistency proof for the predicative second-order system PG, which employs plural quantification and a formulation of Frege's infamous Basic  ...  Nevertheless, these latter are eliminated via substitution by numerals. All this shall suffice to assign denotations to all extension-terms of L .  ... 
doi:10.1007/s11225-011-9311-9 fatcat:v2uvvi6ckfhznbnu6zyknuqaym

Degree quantifiers, bare quantifiers and intensifiers in the midfield: A new look at quantification at a distance

J.-Marc Authier
2016 Glossa  
There is nothing 'long distance' about the semantic composition of QAD; it simply proceeds via adjacency." In this article, I aim to challenge this view.  ...  Nearly all of the theories of Quantification at a Distance (QAD) that have been put forth in the past fifteen years have assumed that degree quantifiers are first merged in the derivation as a midfield  ...  Sentences like (56) should in fact be possible under the polyadic quantification account since the polyadic quantifier would bind the free variable contained in the silent copy of the derived subject,  ... 
doi:10.5334/gjgl.45 fatcat:utmozfzzg5efrmwlvga5zxebmy

The superamalgamation property for reducts of Heyting polyadic algebras with and without equality [article]

Tarek Sayed Ahmed
2013 arXiv   pre-print
We show that several reducts of Heyting polyadic algebras of infinite dimension, with and without equality enjoy various amalgamation properties.  ...  This concept also occurs in polyadic algebras, but unfortunately under a different name, that of compressions.  ...  These lemmata address a very important and key concept in both cylindric and polyadic theories, namely, that of forming dilations and neat reducts (which are, in fact, dual operations.)  ... 
arXiv:1304.0707v1 fatcat:ochmza5agbg4tkt6tsjrgtkceu
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