scholarly journals Complexity of Admissible Rules in the Implication-Negation Fragment of Intuitionistic Logic

10.29007/cll3 ◽  
2018 ◽  
Author(s):  
Petr Cintula ◽  
George Metcalfe
Keyword(s):  
Intuitionistic Logic ◽  
Admissible Rules ◽  
Complete Set

The goal of this paper is to study the complexity of the set of admissible rules of the implication-negation fragment of intuitionistic logic IPC. Surprisingly perhaps, although this set strictly contains the set of derivable rules (the fragment is not structurally complete), it is also PSPACE-complete. This differs from the situation in the full logic IPC where the admissible rules form a co-NEXP-complete set.

Logical connectives for intuitionistic propositional logic

1971 ◽  
Vol 36 (1) ◽  
pp. 15-20 ◽  
Author(s):  
Dean P. McCullough
Keyword(s):  
Intuitionistic Logic ◽  
Propositional Logic ◽  
Classical Type ◽  
Classical Propositional Logic ◽  
Intuitionistic Propositional Logic ◽  
Truth Function ◽  
Logical Connectives ◽  
Complete Set ◽  
Complete Sets

In classical propositional logic it is well known that {7, ⊃ } is a functionally complete set with respect to a two-valued truth function modeling. I.e. all definable logical connectives are definable from 7 and ⊃. Other modelings of classical type propositional logics may have different functionally complete sets; for example, multivalued truth function modelings.This paper examines the question of a functionally complete set of logical connectives for intuitionistic propositional logic with respect to S. Kripke's modeling for intuitionistic logic.

Admissible and derivable rules in intuitionistic logic

1993 ◽  
Vol 3 (2) ◽  
pp. 129-136 ◽  
Author(s):  
Paul Rozière
Keyword(s):  
Intuitionistic Logic ◽  
Sufficient Conditions ◽  
Propositional Calculus ◽  
Admissible Rules ◽  
Intuitionistic Propositional Calculus

This paper gives some sufficient conditions for admissible rules to be derivable in intuitionistic propositional calculus. For example, if the premises are Harrop formulas, the rule is admissible only if it is derivable.In deriving the results, a particular class of substitutes is introduced, which are also useful when dealing with other questions of admissibility.

Bonded Force Constant Derivation of Lysine-Arginine Cross-linked Advanced Glycation End-Products

2018 ◽  
Author(s):  
Anthony Nash ◽  
Nora H de Leeuw ◽  
Helen L Birch
Keyword(s):  
Molecular Dynamics ◽  
Force Constant ◽  
Computational Study ◽  
Force Constants ◽  
Quantum Mechanical ◽  
Advanced Glycation ◽  
Partial Charges ◽  
Cross Links ◽  
Complete Set ◽  
Dynamics Simulations

<div> <div> <div> <p>The computational study of advanced glycation end-product cross- links remains largely unexplored given the limited availability of bonded force constants and equilibrium values for molecular dynamics force fields. In this article, we present the bonded force constants, atomic partial charges and equilibrium values of the arginine-lysine cross-links DOGDIC, GODIC and MODIC. The Hessian was derived from a series of <i>ab initio</i> quantum mechanical electronic structure calculations and from which a complete set of force constant and equilibrium values were generated using our publicly available software, ForceGen. Short <i>in vacuo</i> molecular dynamics simulations were performed to validate their implementation against quantum mechanical frequency calculations. </p> </div> </div> </div>

A flux-based stoichiometric model of enhanced biological phosphorus removal metabolism

1998 ◽  
Vol 37 (4-5) ◽  
pp. 609-613
Author(s):  
J. Pramanik ◽  
P. L. Trelstad ◽  
J. D. Keasling
Keyword(s):  
Phosphorus Removal ◽  
Reaction Network ◽  
Bacterial Biomass ◽  
Enhanced Biological Phosphorus Removal ◽  
Biological Phosphorus Removal ◽  
Stoichiometric Model ◽  
Aerobic Reactor ◽  
Complete Set ◽  
Biological Phosphorus

Enhanced biological phosphorus removal (EBPR) in wastewater treatment involves metabolic cycling through the biopolymers polyphosphate (polyP), polyhydroxybutyrate (PHB), and glycogen. This cycling is induced through treatment systems that alternate between carbon-rich anaerobic and carbon-poor aerobic reactor basins. While the appearance and disappearance of these biopolymers has been documented, the intracellular pressures that regulate their synthesis and degradation are not well understood. Current models of the EBPR process have examined a limited number of metabolic pathways that are frequently lumped into an even smaller number of “reactions.” This work, on the other hand, uses a stoichiometric model that contains a complete set of the pathways involved in bacterial biomass synthesis and energy production to examine EBPR metabolism. Using the stoichiometric model we were able to analyze the role of EBPR metabolism within the larger context of total cellular metabolism, as well as predict the flux distribution of carbon and energy fluxes throughout the total reaction network. The model was able to predict the consumption of PHB, the degradation of polyP, the uptake of acetate and the release of Pi. It demonstrated the relationship between acetate uptake and Pi release, and the effect of pH on this relationship. The model also allowed analysis of growth metabolism with respect to EBPR.

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