scholarly journals Non-idempotent Intersection Types in Logical Form

2020 ◽  
pp. 198-216
Author(s):  
Thomas Ehrhard
Keyword(s):  
Linear Logic ◽  
Logical Form ◽  
Quantitative Information ◽  
Second Order ◽  
Logical System ◽  
Order Types ◽  
Essential Tool ◽  
Intersection Types ◽  
Intersection Rule

AbstractIntersection types are an essential tool in the analysis of operational and denotational properties of lambda-terms and functional programs. Among them, non-idempotent intersection types provide precise quantitative information about the evaluation of terms and programs. However, unlike simple or second-order types, intersection types cannot be considered as a logical system because the application rule (or the intersection rule, depending on the presentation of the system) involves a condition stipulating that the proofs of premises must have the same structure. Using earlier work introducing an indexed version of Linear Logic, we show that non-idempotent typing can be given a logical form in a system where formulas represent hereditarily indexed families of intersection types.

Decision Problems for Second-Order Linear Logic

1997 ◽  
pp. 127-143
Author(s):  
P. D. Lincoln ◽  
A. Scedrov ◽  
N. Shankar
Keyword(s):  
Linear Logic ◽  
Second Order ◽  
Decision Problems ◽  
Order Linear

scholarly journals Nuclear Response to Second-Order Isospin Probes in Connection to Double Beta Decay

Universe ◽  
2020 ◽  
Vol 6 (11) ◽  
pp. 217
Author(s):  
Francesco Cappuzzello ◽  
Manuela Cavallaro
Keyword(s):  
Charge Exchange ◽  
Theoretical Calculations ◽  
Nuclear Matrix Element ◽  
Quantitative Information ◽  
Mass Scale ◽  
Second Order ◽  
Double Beta Decay ◽  
Coupling Constants ◽  
Exchange Reactions ◽  
Double Charge

One of the key ingredients needed to extract quantitative information on neutrino absolute mass scale from the possible measurement of the neutrinoless double-beta (0νββ) decay half-lives is the nuclear matrix element (NME) characterizing such transitions. NMEs are not physical observables and can only be deduced by theoretical calculations. However, since the atomic nuclei involved in the decay are many-body systems, only approximated values are available to date. In addition, the value of the coupling constants to be used for the weak interaction vertices is still an open question, which introduces a further indetermination in the calculations of NMEs. Several experimental approaches were developed in the years with the aim of providing useful information to further constrain the theory. Here we give an overview of the role of charge exchange reactions in this scenario, focusing on second-order processes, namely the double charge exchange (DCE) reactions.

Girard quantaloids

1992 ◽  
Vol 2 (1) ◽  
pp. 93-108 ◽  
Author(s):  
Kimmo I. Rosenthal
Keyword(s):  
General Theory ◽  
Linear Logic ◽  
Logical System ◽  
Partially Ordered

The partially ordered models of linear logic, a logical system developed by J. Y. Girard, turn out to be a class of quantales called Girard quantales. The notion of a quantaloid is a natural categorical generalization of a quantale and is one possible way of keeping track of types. In this paper, Girard quantales are generalized to Girard quantaloids. The general theory is developed and several key examples are studied. Turning our attention to the theory of categories enriched in a bicategory, it is then shown that if G is a Girard quantaloid, then the quantaloids Bim(G), Matr(G), and Mon(G), consisting of G-bimodules, G-matrices and G-monads respectively, are also Girard quantaloids.

scholarly journals The Subtyping Problem for Second-Order Types Is Undecidable

2002 ◽  
Vol 179 (1) ◽  
pp. 1-18 ◽  
Author(s):  
Jerzy Tiuryn ◽  
Paweł Urzyczyn
Keyword(s):  
Second Order ◽  
Order Types

scholarly journals Consideraciones lógico-epistémicas relativas a una forma de conceptualismo ramificado

1991 ◽  
Vol 23 (69) ◽  
pp. 3-25
Author(s):  
Max A. Freund
Keyword(s):  
Formal System ◽  
Second Order ◽  
Order System ◽  
Logical System ◽  
Logical Basis ◽  
Relative Consistency ◽  
Intuitive Interpretation

An intuitive interpretation of constructive knowability is first developed. Then, an epistemic second order logical system (which formalizes logical aspects of the interpretation) is constructed. A proof of the relative consistency of such a system is offered. Next, a formal system of intensional arithmetic (whose logical basis is the aforementioned second order system) is stated. It is proved that such a formal system of intensional arithmetic entails a theorem, whose content would show possible limitations to constructive knowability.

scholarly journals Non-linear Second Order Abstract Categorial Grammars and Deletion

10.29007/644d ◽  
2018 ◽  
Author(s):  
Sylvain Salvati
Keyword(s):  
Natural Language ◽  
Second Order ◽  
Categorial Grammars ◽  
Non Linear ◽  
Intersection Types ◽  
Coherence Spaces

We prove that non-linear second order Abstract Categorial Grammars(2ACGs) are equivalent to non-deleting 2ACGs. We prove this resultfirst by using the intersection types discipline. Then we explainhow coherence spaces can yield the same result. This result showsthat restricting the Montagovian approach to natural languagesemantics to use only $\L I$-terms has no impact in terms of thedefinable syntax/semantics relations.

Analysis of Barriers to Control of Manipulators Within Accessible Output Sets

1995 ◽  
Author(s):  
Edward J. Haug ◽  
Frederick A. Adkins ◽  
Chaoxin Charles Qiu ◽  
Jeng Yen
Keyword(s):  
Quadratic Forms ◽  
Closed Loop ◽  
Position Control ◽  
Quantitative Information ◽  
Second Order ◽  
Velocity Control ◽  
Unilateral Constraints ◽  
Open Chain ◽  
Output Control ◽  
Curves And Surfaces

Abstract Barriers to output control of manipulators, both in the interior and at the boundary of accessible output sets, are analyzed using first and second order Taylor approximations of the output in selected directions as functions of manipulator input. The formulation is valid for both planar and spatial manipulators, with open chain and closed loop structures, and accounts for the effects of unilateral constraints on the range of admissible control inputs. Criteria defining curves and surfaces associated with singular output control of manipulators are extended to define normals to such curves and surfaces. It is shown that output velocity in the direction normal to such curves and surfaces must be zero, so they arc barriers to velocity control in the associated manipulator configuration. Second order Taylor expansion of normal output with respect to input parameters yields quantitative information regarding barriers to output position control. Definiteness properties of the resulting quadratic approximation define directions of admissible and inadmissible outputs. Algorithms for automatically computing the associated quadratic forms and eigenvalues that determine their definiteness properties are presented and illustrated using planar examples.

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