scholarly journals Dependence logic with generalized quantifiers: Axiomatizations

2017 ◽  
Vol 88 ◽  
pp. 90-102 ◽  
Author(s):  
Fredrik Engström ◽  
Juha Kontinen ◽  
Jouko Väänänen
Keyword(s):  
Generalized Quantifiers ◽  
Dependence Logic

scholarly journals Characterizing quantifier extensions of dependence logic

2013 ◽  
Vol 78 (1) ◽  
pp. 307-316 ◽  
Author(s):  
Fredrik Engström ◽  
Juha Kontinen
Keyword(s):  
Expressive Power ◽  
Second Order ◽  
Order Logic ◽  
Generalized Quantifiers ◽  
Dependence Logic ◽  
Second Order Logic

AbstractWe characterize the expressive power of extensions of Dependence Logic and Independence Logic by monotone generalized quantifiers in terms of quantifier extensions of existential second-order logic.

scholarly journals QUANTUM TEAM LOGIC AND BELL’S INEQUALITIES

2015 ◽  
Vol 8 (4) ◽  
pp. 722-742 ◽  
Author(s):  
TAPANI HYTTINEN ◽  
GIANLUCA PAOLINI ◽  
JOUKO VÄÄNÄNEN
Keyword(s):  
Quantum Mechanics ◽  
Completeness Theorem ◽  
Probability Logic ◽  
Bell’S Inequalities ◽  
Dependence Logic ◽  
Logical Approach ◽  
Team Semantics ◽  
Bell's Inequalities

AbstractA logical approach to Bell’s Inequalities of quantum mechanics has been introduced by Abramsky and Hardy (Abramsky & Hardy, 2012). We point out that the logical Bell’s Inequalities of Abramsky & Hardy (2012) are provable in the probability logic of Fagin, Halpern and Megiddo (Fagin et al., 1990). Since it is now considered empirically established that quantum mechanics violates Bell’s Inequalities, we introduce a modified probability logic, that we call quantum team logic, in which Bell’s Inequalities are not provable, and prove a Completeness theorem for this logic. For this end we generalise the team semantics of dependence logic (Väänänen, 2007) first to probabilistic team semantics, and then to what we call quantum team semantics.

scholarly journals A fuzzy syllogistic reasoning schema for generalized quantifiers

2014 ◽  
Vol 234 ◽  
pp. 79-96 ◽  
Author(s):  
M. Pereira-Fariña ◽  
Juan C. Vidal ◽  
F. Dĺaz-Hermida ◽  
A. Bugarĺn
Keyword(s):  
Syllogistic Reasoning ◽  
Generalized Quantifiers

scholarly journals Semantics with Dependent Types for Indefinites

2016 ◽  
Vol 46 (1) ◽  
pp. 173-192
Author(s):  
Justyna Grudzińska
Keyword(s):  
Dynamic Properties ◽  
Formal System ◽  
Dependent Types ◽  
Generalized Quantifiers

Abstract The paper proposes a new semantics with dependent types for indefinites, encompassing both the data related to their exceptional scopal behavior and the data related to their anaphoric (dynamic) properties. The proposal builds on the formal system combining generalized quantifiers ([Mostowski 1957], [Lindström 1966]) with dependent types ([Martin-Löf 1972], [Makkai 1995]) in [Grudzińska & Zawadowski 2014] and [Grudzińska & Zawadowski 2016].

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