scholarly journals Coinductive predicates and final sequences in a fibration

2017 ◽  
Vol 28 (4) ◽  
pp. 562-611 ◽  
Author(s):  
ICHIRO HASUO ◽  
TOSHIKI KATAOKA ◽  
KENTA CHO
Keyword(s):  
Predicate Logic ◽  
Binary Relations ◽  
Transition Systems ◽  
Seminal Work ◽  
Locally Presentable Categories ◽  
Size Restriction ◽  
Constructive Logics

Coinductive predicates express persisting ‘safety’ specifications of transition systems. Previous observations by Hermida and Jacobs identify coinductive predicates as suitable final coalgebras in a fibration – a categorical abstraction of predicate logic. In this paper, we follow the spirit of a seminal work by Worrell and study final sequences in a fibration. Our main contribution is to identify some categorical ‘size restriction’ axioms that guarantee stabilization of final sequences after ω steps. In its course, we develop a relevant categorical infrastructure that relates fibrations and locally presentable categories, a combination that does not seem to be studied a lot. The genericity of our fibrational framework can be exploited for binary relations (i.e. the logic of ‘binary predicates’) for which a coinductive predicate is bisimilarity, constructive logics (where interests are growing in coinductive predicates) and logics for name-passing processes.

RECOGNIZABLE AND LOGICALLY DEFINABLE LANGUAGES OF INFINITE COMPUTATIONS IN CONCURRENT AUTOMATA

1998 ◽  
Vol 09 (03) ◽  
pp. 295-313 ◽  
Author(s):  
MANFRED DROSTE ◽  
DIETRICH KUSKE
Keyword(s):  
Concurrent Programs ◽  
Binary Relations ◽  
Ordered Sets ◽  
Transition Systems ◽  
Infinite Products ◽  
Verification Methods ◽  
Language L ◽  
Rational Expressions ◽  
Second Order Logic ◽  
Monadic Second Order Logic

Automata with concurrency relations [Formula: see text], which occurred in formal verification methods of concurrent programs, are labeled transition systems with a collection of binary relations describing when two actions in a given state of the automaton can happen independently of each other. The concurrency monoid M($\mathcal{A}$) comprises all finite computation sequences of [Formula: see text], modulo a canonical congruence induced by the concurrency relations, with composition as monoid operation. Then M∞($\mathcal{A}$) denotes the set of all infinite products in M($\mathcal{A}$); its elements can be represented by labeled partially ordered sets. Under suitable assumptions on [Formula: see text], we show that a language L in M∞($\mathcal{A}$) is recognizable iff it is definable by a formula of monadic second order logic, and that it is recognizable iff it can be constructed from recognizable languages in M($\mathcal{A}$) using co-rational expressions. This generalizes various recent results in trace theory.

CONCURRENT AUTOMATA AND DOMAINS

1992 ◽  
Vol 03 (04) ◽  
pp. 389-418 ◽  
Author(s):  
MANFRED DROSTE
Keyword(s):  
Concurrent Systems ◽  
Equivalence Classes ◽  
Binary Relations ◽  
Transition Systems ◽  
Operational Model ◽  
Locally Finite ◽  
Natural Domain ◽  
Theoretic Characterization ◽  
Natural Way

We introduce an operational model of concurrent systems, called automata with concurrency relations. These are labeled transition systems [Formula: see text] in which the event set is endowed with a collection of symmetric binary relations which describe when two events at a particular state of [Formula: see text] commute. This model generalizes the recent concept of Stark’s trace automata. A permutation equivalence for computation sequences of [Formula: see text] arises canonically, and we obtain a natural domain [Formula: see text] comprising the induced equivalence classes. We give a complete order-theoretic characterization of all such partial orders [Formula: see text] which turn out to be particular finitary domains. The arising domains [Formula: see text] are particularly pleasant Scott-domains, if [Formula: see text] is assumed to be concurrent, i.e. if the concurrency relations of [Formula: see text] depend (in a natural way) locally on each other, but not necessarily globally. We show that both event domains and dI-domains arise, up to isomorphism, as domains [Formula: see text] with well-behaved such concurrent automata [Formula: see text]. We introduce a subautomaton relationship for concurrent automata and show that, given two concurrency domains (D, ≤), (D′, ≤), there exists a nice stable embedding-projection pair from D to D′ iff D, D′ can be generated by concurrent automata [Formula: see text] such that [Formula: see text] is a subautomaton of [Formula: see text]. Finally, we introduce the concept of locally finite concurrent automata as a limit of finite concurrent automata and show that there exists a universal homogeneous locally finite concurrent automaton, which is unique up to isomorphism.

A Court in Decline? Examining the Regality Court Records of Melrose, Roxburghshire, 1657–84

2020 ◽  
Vol 40 (1) ◽  
pp. 1-16
Author(s):  
Vivienne Dunstan
Keyword(s):  
Seventeenth Century ◽  
Local Community ◽  
Local Population ◽  
Local Area ◽  
Vital Role ◽  
Local Communities ◽  
Court Records ◽  
Seminal Work

McIntyre, in his seminal work on Scottish franchise courts, argues that these courts were in decline in this period, and of little relevance to their local population. 1 But was that really the case? This paper explores that question, using a particularly rich set of local court records. By analysing the functions and significance of one particular court it assesses the role of this one court within its local area, and considers whether it really was in decline at this time, or if it continued to perform a vital role in its local community. The period studied is the mid to late seventeenth century, a period of considerable upheaval in Scottish life, that has attracted considerable attention from scholars, though often less on the experiences of local communities and people.

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.

Neural Transition Systems for Modeling Hierarchical Semantic Representations

2019 ◽  
Author(s):  
Riyaz Bhat ◽  
John Chen ◽  
Rashmi Prasad ◽  
Srinivas Bangalore
Keyword(s):  
Semantic Representations ◽  
Transition Systems

John Henry Newman

2018 ◽  
Author(s):  
Michael D. Hurley
Keyword(s):  
John Henry Newman ◽  
Seminal Work ◽  
Non Fiction ◽  
Prose Style ◽  
Definition Of

Newman has been much vaunted as a ‘master’ of non-fiction prose style, and justly so. His felicity of phrasing is astonishing: so precise, so elegant, so vivid. This chapter admires Newman’s stylistic achievements too, but with a view to explaining why Newman himself baulked at such praise, by insisting instead on the importance of veracity over verbalism. While a number of different writings by Newman are surveyed in the course of the chapter, the argument comes to focus in particular on his seminal work of faith, Grammar of Assent, a book that took him some twenty years to write, which almost killed him, and which best exemplifies his suggestive but enigmatic definition of ‘style’ as ‘a thinking out into language’.

Ecofeminist Biblical Hermeneutics for Cyborgs and the Story of Jezebel

2020 ◽  
pp. 295-311
Author(s):  
Arthur W. Walker-Jones
Keyword(s):  
Digital Media ◽  
Hebrew Bible ◽  
Digital Humanities ◽  
Environmental Crisis ◽  
Biblical Hermeneutics ◽  
Biblical Story ◽  
Seminal Work ◽  
Feminist Interpretation ◽  
Digital Cultures

This chapter examines the Jezebel.com website as a feminist interpretation of the biblical story of Jezebel, in order to discuss the ways digital media make reading more transparent, intertextual, and holistic. Donna Haraway’s article “A Manifesto for Cyborgs” is a seminal work for both ecofeminism and the digital humanities. This articles uses her understanding of the cyborg and naturecultures to argue that Jezebel has become a cyborg online. Cyborgs and digital media could be used to reinforce the nature–culture dualism that is related to male–female dualism and has legitimated patriarchy and the environmental crisis. This chapter, therefore, argues that the identification of cyborg naturecultures in reading both the biblical stories and digital cultures is particularly important for ecofeminist approaches to the Hebrew Bible.

scholarly journals Battery transition systems

2014 ◽  
Vol 49 (1) ◽  
pp. 595-606 ◽  
Author(s):  
Udi Boker ◽  
Thomas A. Henzinger ◽  
Arjun Radhakrishna
Keyword(s):  
Transition Systems
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