A Decision Procedure for Sets, Binary Relations and Partial Functions

2016 ◽  
pp. 179-198 ◽  
Author(s):  
Maximiliano Cristiá ◽  
Gianfranco Rossi
Keyword(s):  
Decision Procedure ◽  
Binary Relations ◽  
Partial Functions

Methods and clinical applications in nuclear cardiology: a position statement

2002 ◽  
Vol 41 (01) ◽  
pp. 3-13 ◽  
Author(s):  
M. Schäfers
Keyword(s):  
Nuclear Cardiology ◽  
Clinical Medicine ◽  
Imaging Techniques ◽  
Cost Savings ◽  
Cost Benefit ◽  
Position Statement ◽  
Electron Beam Tomography ◽  
Partial Functions ◽  
Cost Benefit Ratio ◽  
Medicine Today

SummaryNuclear cardiological procedures have paved the way for non-invasive diagnostics of various partial functions of the heart. Many of these functions cannot be visualised for diagnosis by any other method (e. g. innervation). These techniques supplement morphological diagnosis with regard to treatment planning and monitoring. Furthermore, they possess considerable prognostic relevance, an increasingly important issue in clinical medicine today, not least in view of the cost-benefit ratio.Our current understanding shows that effective, targeted nuclear cardiology diagnosis – in particular for high-risk patients – can contribute toward cost savings while improving the quality of diagnostic and therapeutic measures.In the future, nuclear cardiology will have to withstand mounting competition from other imaging techniques (magnetic resonance imaging, electron beam tomography, multislice computed tomography). The continuing development of these methods increasingly enables measurement of functional aspects of the heart. Nuclear radiology methods will probably develop in the direction of molecular imaging.

FACTOR ANALYSIS OF GEOGRAPHIC COORDINATES AT POINTS OF THE CHANNEL OF A SMALL RIVER ON SPACE IMAGES

2020 ◽  
Author(s):  
Peter Matveevich Mazurkin ◽  
Yana Oltgovna Georgieva
Keyword(s):  
Correlation Coefficient ◽  
Geographical Location ◽  
Small River ◽  
Binary Relations ◽  
Catchment Basin ◽  
Space Images ◽  
The North ◽  
Inverse Effect ◽  
Characteristic Points ◽  
Fractal Representation

The purpose of the article is the analysis of asymmetric wavelets in binary relations between three coordinates at 290 characteristic points from the source to the mouth of the small river Irovka. The hypsometric characteristic is the most important property of the relief. The Irovka River belongs to a low level, at the mouth it is 89 m high, and at the source it is 148 m above sea level. Modeling of binary relations with latitude, longitude, and height has shown that local latitude receives the greatest quantum certainty. In this case, all paired regularities received a correlation coefficient of more than 0.95. Such a high adequacy of wave patterns shows that geomorphology can go over to the wave multiple fractal representation of the relief. The Irovka River is characterized by a small anthropogenic impact, therefore, the relief over a length of 69 km has the natural character of the oscillatory adaptation of a small river to the surface of the Vyatka Uval from its eastern side. This allows us to proceed to the analysis of the four tributaries of the small river Irovka, as well as to model the relief of the entire catchment basin of 917 km2. The greatest adequacy with a correlation coefficient of 0.9976 was obtained by the influence of latitude on longitude, that is, the geographical location of the relief of the river channel with respect to the geomorphology of the Vyatka Uval. In second place with a correlation of 0.9967 was the influence of the height of the points of the channel of the small river on local longitude and it is also mainly determined by the relief of the Vyatka Uval. In third place was the effect of latitude on height with a correlation coefficient of 0.9859. And in last sixth place is the inverse effect of altitude on local latitude in the North-South direction.

A Decision Procedure for Bit-Vector Arithmetic

1998 ◽  
Author(s):  
Clark W. Barrett ◽  
David L. Dill ◽  
Jeremy R. Levitt
Keyword(s):  
Decision Procedure ◽  
Bit Vector

On the action of the implicative closure operator on the set of partial functions of the multivalued logic

2021 ◽  
Vol 31 (3) ◽  
pp. 155-164
Author(s):  
Sergey S. Marchenkov
Keyword(s):  
Closure Operator ◽  
Multivalued Logic ◽  
Partial Functions ◽  
Logical Implication

Abstract On the set P k ∗ $\begin{array}{} \displaystyle P_k^* \end{array}$ of partial functions of the k-valued logic, we consider the implicative closure operator, which is the extension of the parametric closure operator via the logical implication. It is proved that, for any k ⩾ 2, the number of implicative closed classes in P k ∗ $\begin{array}{} \displaystyle P_k^* \end{array}$ is finite. For any k ⩾ 2, in P k ∗ $\begin{array}{} \displaystyle P_k^* \end{array}$ two series of implicative closed classes are defined. We show that these two series exhaust all implicative precomplete classes. We also identify all 8 atoms of the lattice of implicative closed classes in P 3 ∗ $\begin{array}{} \displaystyle P_3^* \end{array}$ .

scholarly journals Finite representability of semigroups with demonic refinement

2021 ◽  
Vol 82 (2) ◽  
Author(s):  
Robin Hirsch ◽  
Jaš Šemrl
Keyword(s):  
Partial Order ◽  
Turing Machines ◽  
Binary Relations ◽  
Finite Representation ◽  
First Order ◽  
Finite Structures ◽  
Finite Base ◽  
Finite Set ◽  
Finite Representability ◽  
Representation Class

AbstractThe motivation for using demonic calculus for binary relations stems from the behaviour of demonic turing machines, when modelled relationally. Relational composition (; ) models sequential runs of two programs and demonic refinement ($$\sqsubseteq $$ ⊑ ) arises from the partial order given by modeling demonic choice ($$\sqcup $$ ⊔ ) of programs (see below for the formal relational definitions). We prove that the class $$R(\sqsubseteq , ;)$$ R ( ⊑ , ; ) of abstract $$(\le , \circ )$$ ( ≤ , ∘ ) structures isomorphic to a set of binary relations ordered by demonic refinement with composition cannot be axiomatised by any finite set of first-order $$(\le , \circ )$$ ( ≤ , ∘ ) formulas. We provide a fairly simple, infinite, recursive axiomatisation that defines $$R(\sqsubseteq , ;)$$ R ( ⊑ , ; ) . We prove that a finite representable $$(\le , \circ )$$ ( ≤ , ∘ ) structure has a representation over a finite base. This appears to be the first example of a signature for binary relations with composition where the representation class is non-finitely axiomatisable, but where the finite representation property holds for finite structures.

An Automata-Theoretic Decision Procedure for Propositional Temporal Logic with Since and Until1

1992 ◽  
Vol 17 (3) ◽  
pp. 271-282
Author(s):  
Y.S. Ramakrishna ◽  
L.E. Moser ◽  
L.K. Dillon ◽  
P.M. Melliar-Smith ◽  
G. Kutty
Keyword(s):  
Temporal Logic ◽  
Decision Procedure ◽  
Linear Time ◽  
Computer Systems ◽  
Hierarchical Abstraction ◽  
Soundness And Completeness

We present an automata-theoretic decision procedure for Since/Until Temporal Logic (SUTL), a linear-time propositional temporal logic with strong non-strict since and until operators. The logic, which is intended for specifying and reasoning about computer systems, employs neither next nor previous operators. Such operators obstruct the use of hierarchical abstraction and refinement and make reasoning about concurrency difficult. A proof of the soundness and completeness of the decision procedure is given, and its complexity is analyzed.

Sign in / Sign up

Export Citation Format

Share Document