Primitive Symbol Research Articles

Automated Degradation Diagnosis in Character Recognition System Subject to Camera Vibration

Degradation diagnosis plays an important role for degraded character processing, which can tell the recognition difficulty of a given degraded character. In this paper, we present a framework for automated degraded character recognition system by statistical syntactic approach using 3D primitive symbol, which is integrated by degradation diagnosis to provide accurate and reliable recognition results. Our contribution is to design the framework to build the character recognition submodels corresponding to degradation subject to camera vibration or out of focus. In each character recognition submodel, statistical syntactic approach using 3D primitive symbol is proposed to improve degraded character recognition performance. In the experiments, we show attractive experimental results, highlighting the system efficiency and recognition performance by statistical syntactic approach using 3D primitive symbol on the degraded character dataset.

A Discussion on Finite Quasi-cardinals in Quasi-set Theory

Quasi-set theory Q is an alternative set-theory designed to deal mathematically with collections of indistinguishable objects. The intended interpretation for those objects is the indistinguishable particles of non-relativistic quantum mechanics, under one specific interpretation of that theory. The notion of cardinal of a collection in Q is treated by the concept of quasi-cardinal, which in the usual formulations of the theory is introduced as a primitive symbol, since the usual means of cardinal definition fail for collections of indistinguishable objects. In a recent work, Domenech and Holik have proposed a definition of quasi-cardinality in Q. They claimed their definition of quasi-cardinal not only avoids the introduction of that notion as a primitive one, but also that it may be seen as a first step in the search for a version of Q that allows for a greater representative power. According to them, some physical systems can not be represented in the usual formulations of the theory, when the quasi-cardinal is considered as primitive. In this paper, we discuss their proposal and aims, and also, it is presented a modification from their definition we believe is simpler and more general.

Efficient timing and frequency offset estimation scheme for OFDM systems

A new training symbol weighted by pseudo-noise(PN) sequence is designed and an efficient timing and frequency offset estimation scheme for orthogonal frequency division multiplexing(OFDM) systems is proposed. The timing synchronization is accomplished by using the piecewise symmetric conjugate of the primitive training symbol and the good autocorrelation of PN weighted factor. The frequency synchronization is finished by utilizing the training symbol whose PN weighted factor is removed after the timing synchronization. Compared with conventional schemes, the proposed scheme can achieve a smaller mean square error and provide a wider frequency acquisition range.

Set constructors, finite sets, and logical semantics

The use of sets in declarative programming has been advocated by several authors in the literature. A representation often chosen for finite sets is that of scons, parallel to the list constructor cons. The logical theory for such constructors is usually tacitly assumed to be some formal system of classical set theory. However, classical set theory is formulated for a general setting, dealing with both finite and infinite sets, and not making any assumptions about particular set constructors. In giving logical-consequence semantics for programs with finite sets, it is important to know exactly what connection exists between sets and set constructors. The main contribution of this paper lies in establishing these connections rigorously. We give a formal system, called SetAx, designed around the scons constructor. We distinguish between two kinds of set constructors, scons(x, y) and dscons(x, y), where both represent { x} ∪ y, but x ϵ y is possible in the former, while x ∉ y holds in the latter. Both constructors find natural uses in specifying sets in logic programs. The design of SetAx is guided by our choice of scons as a primitive symbol of our theory rather than as a defined one, and by the need to deduce non-membership relations between terms, to enable the use of dscons. After giving the axioms SetAx, we justify it as a suitable theory for finite sets in logic programming by (i) showing that the set constructors indeed behave like finite sets; (ii) providing a framework for establishing the correctness of set unification; and (iii) defining a Herbrand structure and providing a basis for discussing logical consequence semantics for logic programs with finite sets. Together, these results provide a rigorous foundation for the set constructors in the context of logical semantics.

Strong completeness of the Lambek Calculus with respect to Relational Semantics

First of all, let us define the language of LC. Given a denumerable set P of primitive symbols, we let the set of formulae FormLC be the smallest set containing every primitive symbol and closed under “\”, “/”, and “•”, i.e., if A,B ∈ FormLC, then A\B, A/B, A•B ∈ FormLC. The set of sequents is the set of all expressions of the form A1, . . . , An ⇒ A0 where n is a positive integer and Ai ∈ FormLC for each i ≤ n. LC is given by the following axiom and rules of inference, where A, B, C stand for formulae and x, y, z stand for finite sequences of formulae including the empty sequence unless the contrary is asserted. Axiom: (0) A⇒ A .

An Inconsistency in Kassler's First Twelve-Note-Class System

In a paper1 entitled Toward a theory that is the twelve-note-class system Michael Kassler constructs several formal systems, of which the first, denoted by R1, has twelve primitive symbols, one formation rule, an axiom, and three rules of inference. In an effort to translate the theory from the language of symbolic logic, in which it is couched, into the algebraic language of mappings and other relations, I have discovered an apparent inconsistency in the system. The algebraic study is contained in my thesis2 for the M.A. degree. Below I offer a short version, in Kassler's language, presenting the primitive basis of R1, together with the relevant definitions, and exhibiting the inconsistency in the form of a counter-example of Kassler's principal metatheorem. The twelve primitive symbols are: 0 1 2 3 4 5 6 7 8 9 a b. A formula is defined to be a non-empty finite string of occurrences of primitive symbols. The formation rule is: r is a wff (well-formed formula) if every primitive symbol occurs in r. The axiom is: 0123456789ab. In order to state the rules of inference, several preliminary definitions are needed. First, the dimension of a formula is the number of tokens (i.e., of occurrences of primitive symbols) in it; e.g., the dimension of 2332 is four. Given a formula r of dimension c and a formula A of dimension d, r is a subformula of A if there is a set S of c positive integers, each less than or equal to d, such that if 1 ? i ? c then the ith token in r is the jth token in A, where j is the least element of S that is greater than exactly i 1 elements of S; such a set S is called a determining set of r from A. Kassler gives this example: if r is 918132 and A is 9.13891338725 then (6, 4, 1, 2, 8, 11) is a determining set of the subformula r from the formula A.

Tense logic for discrete future time

Prior has conjectured that the tense-logical system Gli obtained by adding to a complete basis for the classical propositional calculus the primitive symbol G, the definitionsDf. F: Fα = NGNαDf. L: Lα = KαGα,and the postulatesis complete for the logic of linear, infinite, transitive, discrete future time. In this paper it is demonstrated that that conjecture is correct and it is shown that Gli has the finite model property: see [4]. The techniques used are in part suggested by those used in Bull [2] and [3]:Gli can be shown to be complete for the logic of linear, infinite, transitive, discrete future time in the sense that every formula of Gli which is true of such time can be proved as a theorem of Gli. For this purpose the notion of truth needs to be formalized. This formalization is effected by the construction of a model for linear, infinite, transitive, discrete future time.

On comparison of finite algebras

Introduction. In this paper we shall describe an effective procedure to determine in a finite number of steps whether two abstract algebras A' and of finite order have: (i) the same set of laws, (ii) the set of laws of one of them is included in the set of laws of the other, (iii) distinct sets of laws, (iv) overlapping sets of laws. The procedure is a generalization of certain results obtained by the author in case of truth-tables.' Some parts of the paper On the structure of finite algebras by G. Birkhoff2 will be presupposed, namely: (i) the definition of an abstract algebra A = (T, F) and of its order (?2, pp. 433-434), (ii) the definition of the direct product of abstract algebras (?7, pp. 437-438), (iii) the definition of an abstract algebra of species 1, and of a uniform operator (?8), (iv) the definition of a function 4 of rank n associated with the speciesl, (?9, Definition 2), (v) the idea of a substitution t of elements of an algebra for each primitive symbol of a function 4 and of the resulting value t(4) of the function (?9, p. 439), (vi) the definition of a law of an algebra (?9, Definition 3), (vii) the idea of a law of a set of algebras (?9, p. 439), (viii) the theorem that the set of laws of any aggregate of algebras A is the same as that of the direct product A of all the A (Corollary 2, p. 440). The notation used by Birkhoff in the paper referred to will be followed without further explanation. L(Ao) will stand for the set of laws of any algebra Ao.