bluuebunny/crossref_metadata_2025_split huggingface dataset:
Adding a temporal dimension to a logic system
Authors: Gabbay Dov M , Hodkinson Ian , Reynolds Mark 
Published: November 2023

Abstract
We introduce a methodology whereby an arbitrary logic system L can be enriched with temporal features to create a new system T(L). The new system is constructed by amalgamating L with a pure propositional temporal logic T (such as linear temporal logic with ‘Since’ and ‘Until’) in a special way. We refer to this method as ‘adding a temporal dimension to L’ or just ‘temporalizing L’.We show that the logic system T(L) preserves several properties of the original temporal logic such as soundness, completeness, separation, and decidability.
Post Completeness
Authors: Chagrov Alexander , Zakharyaschev Michael 
Published: November 2023

Abstract
A logic Lis said to bem-reditcibleif, for every formulaφ (q1, ... , qn) ∉ L,there exist formulasψ1 (p1, … , Pm), … , ψn (p1, … , Pm)such that A logic is calledreducibleif it is m-reducible for somem&lt;w.
Concrete process algebra
Authors: Winskel Glynn , Nielsen Mogens 
Published: November 2023

Abstract
Concurrency theory is the branch of computer science that studies the mathematics of concurrent or distributed systems. In concurrency theory, the design of such mathematics is studied and issues concerning the specification and verification of such systems are analysed. Often, a concurrent system is called a process. In order to analyse a large and complex process it is desirable to be able to describe it in terms of smaller and simpler processes. Thus, it seems natural to have some simple processes—the ones that are not subject to further investigation—and operators on them to compose larger ones thus resulting in an algebraic structure. In order to reason about large processes it is often useful to have a set of basic identities between processes at one’s disposal. The most relevant identities among them are normally called axioms. The axiomatic and algebraic point of view on concurrency theory is widely known as process algebra.
Introduction
Authors: Clark Malcolm 
Published: November 2023

Abstract
Tex predates the current concern with microcomputers. This is both a boon and a bane. Its origins lie, in part, in a series of books, The Art of Computer Programming, written by Donald Knuth. This is a projected seven-volume work, as yet incomplete. The first volume was published in 1968, to be followed by Volume 2 in 1969, and Volume 3 in 1973. As might be inferred from the title of the series, the books contain an appreciable amount of mathematics, of one sort or another.
Further rules
Authors: Clark Malcolm 
Published: November 2023

Abstract
The next example (Figure 16.1) is deceptively simple. What it introduces are two quite important topics. The ‘lesser’ is that it is relatively straightforward to align on a decimal point, simply by treating the integer part as one column and the fractional part (including the decimal) as another column. There are possible refinements on this so that the decimal point itself is always included, but this is inappropriate in this example.
More detailed fonts
Authors: Clark Malcolm 
Published: November 2023

Abstract
There is an area which we have hardly touched, that of the position of characters in a font. The characters in a font may be accessed in a number of ways. We are accustomed to the ‘normal’ way, by actually specifying the character - a, b, c, similarly,some characters are accessed through commands Since there are 128 characters in Computer Modern, it is convenient to divide the table into groups of eight or 16. There is a convenient way to refer to octal (base 8) or hexadecimal (base 16) numbers, rather than decimal numbers. For example, the following are equivalent: \char' 152 and \char"6A. An octal number is preceded by a ', while a hexadecimal number is preceded by a 11 Note that the hexadecimal numbers use the upper-case alphabetic characters. Using lower-case will lead to trouble.
Last words
Authors: Clark Malcolm 
Published: November 2023

Abstract
What will the future of Tex be? Will there be a Tex4 to follow the Tex3 of 1989? It is clear from the statements made by Knuth that he is unwilling to consider this possibility. It may not be impossible, since the change to Tex3 seemed impossible immediately before the Stanford conference at which Knuth announced his intention to make one last major change (the ability for Tex to handle 8-bit characters rather than 7-bit), and a number of less significant (though sometimes extremely useful) changes. Nevertheless, Knuth has said that Tex3 is ‘frozen’, or at least, the only changes which will be made are corrections to the code.
Extors in Projective Space
Authors: Goldman William m. 
Published: November 2023

Abstract
The last two chapters deal with the general theory of bisector intersections. This chapter discusses a class of real hypersurfaces (called “extors”) in complex projective space which extend and generalize bisectors in complex hyperbolic and elliptic geometry. The complex projective theory of extors is simpler than that of bisectors in the metric geometries.
Intersections of Bisectors
Authors: Goldman William m. 
Published: November 2023

Abstract
In real hyperbolic space, bisectors are totally geodesic and so are their intersections. In particular bisector intersections are necessarily connected. However, in complex hyperbolic geometry, this is no longer true. We have already discussed two cases of bisector intersections: cospinal pairs (where the spines lie in a common complex geodesic, see §5.3.1) and comeridianal pairs (where the spines lie in a common meridian, see §5.3.5). Cospinal families of bisectors arose from the orthogonal projections onto complex geodesics. Comeridianal pairs arose in the discussion of Cartan’s configuration of seven ℝ-circles characterizing triples of points lying on a chain.
Systems of several particles
Authors: Hannabuss Keith 
Published: November 2023

Abstract
One often wants to study systems, such as the helium atom of Sections 12.3 and 14.2, that contain more than one particle. We describe two-particle systems by a wave function, ψ (r1, r2), where r1 is the position of the first particle, and r2 that of the second. If we interchange the two particles, then the wave function becomes ψ (r2, r1).
(16.1)
Indefinite Scalar Products
Authors: Lancaster Peter , Rodman Leiba 
Published: November 2023

Abstract
Our geometric notions of orthogonality and angle extend to ∈n and more general spaces with the aid of a (standard) scalar product. A more general concept has many useful applications, but requires us to abandon some of that geometric intuition. We have in mind the indefinite scalar products of the present chapter. In particular, they play vital parts in the analysis of Riccati equations with the symmetries among the coefficients that arise so frequently in practice. Furthermore, the analysis of Riccati equations with complex coefficients, or with real coefficients, demand careful preparations in the context of complex and real spaces, respectively.
Matrix Theory and Control
Authors: Lancaster Peter , Rodman Leiba 
Published: November 2023

Abstract
The ideas and theory presented in this chapter will play important parts in our study of Riccati equations. They revolve around the concepts of controllable (and observable) matrix pairs. The importance of these concepts was recognized in the early years of development of control theory and it was in that context that the terms “controllable” and “observable” arose and have some physical meaning. Our approach uses linear algebra in the development of these concepts because it is this understanding that is required in the sequel. Their significance in the context of systems theory and control is mentioned as the chapter progresses, but is not given complete mathematical development.
H∞ Control Problems
Authors: Lancaster Peter , Rodman Leiba 
Published: November 2023

Abstract
Clearly, the minimum of (1) coincides with the greatest lower bound of the set of positive numbers γ for which (2) is satisfied for some admissible feedback K. Control problems in the form (2) are the subject of this chapter. In recent years, H∞ control problems in various guises have become the subjects of intensive research, mainly by electrical engineers. Hundreds of research papers (and some books) using various approaches to the subject have appeared. We mention the sources Francis (1987), and Kaashoek and Ran (1991), though it cannot be claimed that they cover more than a fraction of the significant work in the area. Other important sources are mentioned in the notes of Section 20.4. It turns out that one successful approach to H00 control problems involves algebraic Riccati equations of continuous type. Here, we treat two simple cases of the so-called “standard problem” of H∞ control, and use the Riccati equation as the main tool for their solution.
Contractive Rational Matrix Functions
Authors: Lancaster Peter , Rodman Leiba 
Published: November 2023

Abstract
In this chapter we study strict contractions. In particular, realizations of strict contractions are characterized, and their minimal unitary completions are described. It will be seen that a continuous algebraic Riccati equation (of the type studied in Part II) and its hermitian solutions play a crucial role in the analysis of strict contractions.
The Matrix Sign Function
Authors: Lancaster Peter , Rodman Leiba 
Published: November 2023

Abstract
It has been shown in Chapter 7 that (under suitable hypotheses) the hermitian solutions of this Riccati equation are intimately connected to certain n dimensional invariant subspaces of M and, in particular, to the spectral sub space M+ of M corresponding to eigenvalues in the open right half-plane (see Theorem 7.6.2, for example).
Predicate calculus
Authors: Ince D C 
Published: November 2023

Abstract
To show how predicate calculus can represent statements about col¬ lections of objects. To describe some rules of inference in the predicate calculus. To show how predicate calculus can be used for program specification. In the previous chapter propositional calculus was described. System specifications and statements of requirements were used as concrete examples of its utility. It was stressed that the examples used were artificial in the sense that they were small. However, the examples were artificial in another respect. They were carefully chosen so that they could be expressed in propositional calculus. Unfortunately, the propositional calculus alone is an inadequate medium for expressing many system specifications.
Set theory
Authors: Ince D C 
Published: November 2023

Abstract
To introduce the idea of a set as a collection of objects. To describe the important set operators. To outline how sets and predicate calculus can be combined to produce mathematical specifications. To describe some rules of inference involving sets. The previous sections of this book have concentrated on using propositional or predicate calculus for describing the functions of a software system. For example, you have now been given the mathematical tools to express the essence of the paragraph lf all the monitoring valves are functioning and at least one computer is on-line, then, provided the system is in a functioning state, the header line will be displayed on all the VDUs attached to the system.
The specification language Z
Authors: Ince D C 
Published: November 2023

Abstract
To describe the schema, the main structuring device in the Z specification language. To describe how schemas can be included within each other. To outline how software systems can be described in the Z specification language. Although in the previous chapters computer systems have been described in precise terms, there has been little stress on the syntax of the mathematical notations used. This part of the book remedies this state of affairs. It describes a language called Z which is based on typed set theory and which allows a concise expression of the functional properties of computer systems. One of the principal features of Z is an object known as a schema.
Some small Z examples
Authors: Ince D C 
Published: November 2023

Abstract
To describe some small but relatively realistic examples of Z specifications. This section describes three examples of Z specifications. Each specification describes a part of a relatively realistic software system, with some degree of simplification introduced in order to keep the chapter to a manageable size. One of the more important parts of a computer’s operating system is the subsystem which maintains files which have been created by users. Part of the filing subsystem is the block handler. Files in the file store will be made up of blocks of storage which are held on some file storage device. During the operation of the computer, files will be created and deleted. This means that, in the first case, blocks will be needed to form a file and, in the second case, blocks will be released from a file ready for use in another file. In order to cope with this the filing subsystem will maintain a reservoir of unused blocks, and will also keep track of blocks which are currently in use. When blocks are released from a deleted file they are normally added to a queue of blocks waiting to be added to the reservoir of unused blocks. This is shown in Figure 11.1.
A large Z specification
Authors: Ince D C 
Published: November 2023

Abstract
To revise many of the concepts described in the previous three chapters. To show how a large Z specification might be structured. The purpose of this chapter is to demonstrate some of the power of the schema calculus in incrementally describing a system and to describe how error processing can be accommodated in a Z specification. The final part of the chapter describes one way of organizing a Z specification and outlines how natural language can be used in conjunction with schemas. The specification described in the chapter is for an automated system for a university library. Only selected parts of the statement of requirements are shown; for example, parts 2.8 to 2.11 dealing with the requirements for microfiche hard copy are omitted.
Lowenheim–Skolem theorems and their consequences
Authors: Manzano María 
Published: November 2023

Abstract
In 1915 Lowenheim proved that if a formula is satisfiable, then it has a countable model. The various statements of the Lowenheim–Skolem theorems which appear in this chapter are successive reinforcements of this initial theorem. Many of these theorems were proved even before model theory had obtained citizenship, and by methods which were very different from those which became commonplace afterwards. The proofs that I give are, with slight modifications, those from Tarski and Vaught’s (1957).
Abductive reasoning in three-valued logic for knowledge bases
Authors: Mathieu Philippe , Delahaye Jean-Paul 
Published: November 2023

Abstract
In this chapter we study the case of monotonic rule-based systems which use a forward chaining algorithm to make deductions and a query algorithm to compute queries to be asked of the user in order to draw closer to the expected goal (as Guru [11], IS [12] or Nexpert [18]). Unfortunately, in many systems the query algorithm is not consistent with the deduction algorithm. Queries asked by these systems are often useless. We show that computing a query for these systems is equivalent to abductive reasoning in three-valued logic and we propose a formalization of useful queries for expert systems. We give two definitions of intelligent queries and two levels on which to compute them: the logical level which aims at computing a list of intelligent queries, and the heuristic level which aims at choosing which query on that list it will ask of the user.
Updates and subjunctive queries
Authors: Grahne Gösta , Mendelzon Alberto 0. 
Published: November 2023

Abstract
A subjunctive query of the form ϕ &gt; Ψ means ‘if ϕ were true in the knowledgebase, would Ψ also necessarily be true?’ We propose the following semantics for subjunctive queries: ϕ &gt; Ψ will hold in the current knowledgebase T if Ψ holds in the result of updating T with ϕ . This is known as the Ramsey test in philosophy. We adapt the model checking approach of Halpern and Vardi: a knowledgebase is a finite set of finite sets of positive facts interpreted in a closed world setting. We then use Winslett’s possible models approach to give semantics to knowledgebase updates, and we introduce a query language which is essentially propositional logic, augmented with a subjunctive conditional that has an intensional interpretation in our model. We show that query answering and update can be performed in polynomial time in the size of the knowledgebase. However, query equivalence is shown to be complete in polynomial space, and this is also the complexity of query answering as a function of query size. We give a sound axiomatization of query equivalence and show that the update operator satisfies the postulates for updates adapted by Katsuno and Mendelzon from the Alchourr6n-Gardenfors-Makinson belief revision postulates.
Interior point algorithms for network flow problems
Authors: Resende Mauricio G C , Pardalos Panos M 
Published: November 2023

Abstract
A large number of problems in transportation, communications and manufacturing can be modelled as network flow problems. In these problems one seeks to find the most efficient, or optimal, way to move flow (e.g. materials, information, buses, electrical currents) on a network (e.g. postal network, computer network, transportation grid, power grid). Many of these optimization problems are special classes of linear programming problems, with combinatorial properties that allow the development of efficient solution techniques. In this chapter, we limit our discussion to linear network flow problems. For a treatment of non-linear network flow problems, the reader is referred to [17, 28, 29, 48].
What is a Logical System?
Authors: Gabbay D M 
Published: November 2023

Abstract
There is an increasing demand from computer science, linguistics and philosophy for a variety of logical systems. This is prompted by the extensive applications of logic in theoretical computer science, artificial intelligence and logic programming. In these fields there is a growing need for a diversity of semantically meaningful and algorithmically presented logical systems which can serve various applications. Therefore renewed research activity is being devoted to analysing and tinkering with old and new logics.
Introduction
Authors: Russ Steve 
Published: November 2023

Abstract
Bernard Bolzano was a Christian humanist who devoted a lifetime of thought and writing to a far-reaching and wide-ranging reform of the representation, organization, and discovery of knowledge. He was ordained as a Catholic priest in 1805 and thereafter, for almost fifteen years, he held a university post in Prague lecturing in theology and giving regular ‘edifying discourses’ to both the students and the public. He was eventually dismissed from his post by the Hapsburg Emperor, Franz I, because his public views, on social and political issues were deemed dangerously liberal, and his theological views even heretical.
Geometry and Foundations
Authors: Russ Steve 
Published: November 2023

Abstract
The first of Bolzano’s publications (BG), on geometry, has several passages treating foundational or philosophical matters. His next publication (BD) on the methodology of mathematics was explicitly directed at addressing particularly the problems of geometry; it seems natural therefore to group these two together. The later work DP includes, curiously, several groups of geometrical definitions that are not actually used in the work itself, but offer a striking proposal for the problem of giving satisfactory definitions of geometric extensions (such as line, surface, and solid). A common theme connecting these three works is what Johnson calls Bolzano’s ‘definitional problem’ (the problem is that of defining the geometric extensions just mentioned, see Johnson (1977)).
A new statistical approach to granular mixtures
Authors: Mehta Anita , Edwards S F 
Published: November 2023

Abstract
There has been great interest recently in the theoretical (Edwards 1988; de Gennes 1988; Mehta and Edwards 1989) and experimental (Douady et al. 1989; Evesque and Rajchenbach 1989; Jaeger et al. 1989) properties of granular materials. This has concerned itself with the statics-how such materials pack, what configurations are observed as a function of their typical parameters-as well as the dynamics-the statistics of the avalanches observed when a sandpile is perturbed, the nature of the instabilities observed as a function of the frequency and amplitude of the perturbation-of such systems.
Spatial and spectral properties of fractons in percolating structures
Authors: Burston R A , Hughes, G D , Lambert C J 
Published: November 2023

Abstract
During the past 10 years there have been many papers aimed at elucidating the properties of random percolating structures. Many of these have dealt with static exponents characterizing properties such as elasticity, conductivity, or mass density. More recently, attention has shifted towards dynamical or quantum properties, such as the density of states per unit volume (DOS) or degree of localization of fracton modes.
The S = 1 quantum spin chain: some exact and numerical results
Authors: Paczek D , Parkinson J B 
Published: November 2023

Abstract
There has been great interest recently in quantum spin chains with S = 1. Much of this work was stimulated by Haldane’s (1983a, b) discussion of the isotropic Heisenberg model for which he predicted the existence of a disordered ground state (i.e. one in which the correlations decay exponentially) and a gap to the first excited state at k = n.
We consider a system with isotropic Heisenberg and biquadratic exchange, and a magnetic field, described by the Hamiltonian.
Single- and two-particle interference
Authors: Loudon Rodney 
Published: November 2023

Abstract
The reconciliation of wave-like optical interference phenomena with the particle-like properties of the quantized radiation field has intrigued physicists since the early years of the present century. Two main topics of discussion have been the effect of very low light levels-of the order of one photon at a time in the interferometer-on the interference fringes, and the possibility of determining which of the two optical paths through the interferometer were taken by the photons that produce the fringes. The first experiment with very low light levels was performed by Taylor (1909) at the instigation of J. J. Thomson. He found that Young’s interference fringes persisted when the low light levels were compensated by long photographic exposure times.
Trends within hydrogenic species: an empirical approach
Authors: Goltzene A , Schwab C 
Published: November 2023

Abstract
In contrast to the wealth of theoretical approaches developed for the computation of energy levels, the ab initio calculations of the electronic structures of defects in a crystal have lagged behind. This situation might be surprising for the experimentalist as a number of spectroscopic data are usually less exploited than they could be. For instance, in electron paramagnetic resonance (EPR), once the features of the spectra related to the number of components and symmetry have been taken into account, the values of the splitting parameters or Lande factors usually remain ignored. This has, however, a practical consequence as it leads to an inability to deal properly with the problem in the case of unresolved hyperfine spectra even if met in promising compound semiconductors such as the 111-V materials.