Order Predicate Research Articles

The Subalgebra Lattice of A Finite Diagonal–Free Two–Dimensional Cylindric Algebra

Diagonal–free two–dimensional cylindric algebras (Df2−algebras for short) are Boolean algebras enriched with two existential quantifiers which commute. Df2−algebras were introduced by A. Tarski, L. Chin and F. Thompson with the purpose of providing an algebraic device for the study of the first–order predicate calculus with two variables. This work is devoted to problems related to finite Df2−algebras. More precisely, we study and describe the family of subalgebras of a given finite Df2−algebra. Then, identifying the algebras of this family which are isomorphic, we provide a full description of the lattice of all non–isomorphic subalgebras of a given finite Df2−algebra.

AI by Any Other Name [President’s Message

Hi all, To borrow from The Bard, what’s in a name? The world is awash with the hype, the reality, the potential, and the concerns of Artificial Intelligence. But what constitutes AI? That depends on who, and when, you ask. When I was a kid (academically speaking), tasked with teaching a course on AI, I “knew” what it was: systems with propositions consisting of discrete symbols, manipulated through first order predicate calculus, sometimes with a helping of probability on the side. There were languages and hardware developed to assist in that enterprise. So, when the IEEE Neural Networks Council/Society changed its name to the IEEE Computational Intelligence Society, it made perfect sense to me that CI was different from AI since the underlying models were rooted in numeric and functional representations, producing a nice crisp partition of techniques.

From Logic to Functional Logic Programs

AbstractLogic programming is a flexible programming paradigm due to the use of predicates without a fixed data flow. To extend logic languages with the compact notation of functional programming, there are various proposals to map evaluable functions into predicates in order to stay in the logic programming framework. Since amalgamated functional logic languages offer flexible as well as efficient evaluation strategies, we propose an opposite approach in this paper. By mapping logic programs into functional logic programs with a transformation based on inferring functional dependencies, we develop a fully automatic transformation which keeps the flexibility of logic programming but can improve computations by reducing infinite search spaces to finite ones.

Kişisel Beslenme Planlamasina Yönelik Web Tabanli Uzman Sistem Tasarimi ve Uygulamasi

Recently, expert systems have been used in different fields for different purposes in order to respond to the changing user needs with the rapid development of information and communication technologies. The most important of these can be listed as interpretation, prediction, diagnosis, design, planning, imaging, debugging, maintenance, education and control. With the increase in the use of expert systems in the field of healthcare, expert systems are not only used for diagnosis and treatment, but also act as a decision support system. Today, there are many software and approaches for nutrition program planning on the basis of nutrition-oriented practices. In particular, rule-based or case-based expert systems are frequently used in the field of nutrition. The aim of the research is to develop a web-based expert system prototype in the field of nutrition with a rule-based system approach using the Prolog development environment. For this purpose, because of clear and neat syntax, one of the expert system programming languages based on "first order predicate calculus" that is Prolog, PHP for web and in the design phase; Bootstrap framework were preferred. For data visualization, data is retrieved from MySQL database. The application developed within the scope of the research is expected to contribute to the efficient implementation of nutrition planning, especially for institutions with insufficient human experts. In this sense, a system that offers personalized nutrition program recommendations for people of different ages, genders, heights, weights and therefore different body mass indexes has been developed. Thus, considering the benefits of proper nutrition, it is expected that the developed system will help the dietitian in the process of determining the nutrition program/meal planning, and for the patients in the processes of maintaining and monitoring it.

Logic and the Mathematic Model of the Subject-Area Description for Corporate Information Systems

Aiming to build and receive a logic-mathematical substantiation and model of the process of constructing the description of any subject area for corporate information systems, the authors divided the subject area for building the system into constituent elements and the relationships between them. Using discrete mathematics methods to the graphs and two-seater predicates of the first order, we built an interconnected model of the subject area. Logical and mathematical models were built upon the main components of the subject area. Based on a technique used to construct its description, the use of the graphical description, combined with the application of transformation in a semantic model of the predicate type, allows us to use further the received model for constructing the normalized databases. The research reveals that constructing the qualitative description of the subject domain of the corporate automated information system requires us to use some consecutive iterations. Logic and mathematical models allow us to construct a general view of the description of the subject area of the corporate automated information system. Further, this generalized model can be transferred to absolutely any concrete subject area. The advantage of constructing the description of the subject area in the form of the predicate type’s semantic model is the integral sight at all considered subject areas, as information representation in the integral form is better perceived. When constructing such a graph, there is a possibility of completely restoring missing logical links. The purpose of the research is to describe the subject area of the corporate system using the graph form of representation. The novelty lies in developing information support model designed for managing processes of acquiring and using knowledge (this model allows to consider usefulness of information elements and didactic connections between elements) and in approach to estimation of achieving information support goals with the use of graphs describing the subject area of corporate system.

Computational Complexity of Intensional Emotive Constructions, (In)tractability and Natural Language Processing

This paper will focus on linguistic constructions involving intensional emotive predicates in order to assess the computational complexity of such constructions based on the features of intensional elements in such constructions. It will be first shown that linguistic constructions vary as a function of the nature of intensional elements involved in such constructions. The important insights derived from these facts will be then carried forward for an exploration of the computational complexity of intensional emotive constructions which can be seen to co-vary in complexity scales with the number of intensional elements or features of intensional elements. Possible ramifications emanating from this for the cognitive tractability of semantic contents and for natural language processing will be offered at the end of the paper.

Using logic programming for theory representation and scientific inference

The aim of this paper is to show that logic programming is a powerful tool for representing scientific theories and for scientific inference. In a logic program it is possible to encode the qualitative and quantitative components of a theory in first order predicate logic, which is a highly expressive formal language. A theory program can then be handed to an algorithm that reasons about the theory. We discuss the advantages of logic programming with regard to building formal theories and present a novel software package for scientific inference: Theory Toolbox. Theory Toolbox can derive any conclusions that are entailed by a theory, explain why a certain conclusion follows from a theory, and evaluate a theory with regard to its internal coherence and generalizability. Because logic is, or should be, a cornerstone of scientific practice, we believe that our paper can make an important contribution to scientific psychology.

Application of fuzzy logic for an enterprise production activity management

For knowledge representation and solving problems of qualitative nature, an applied calculus of fuzzy predicates of the first order has been developed. This theory and methods were used to create an expert system for scientific research in the field of molecular spectroscopy, as well as for a number of other subject areas. One of these areas is the planning and management of the enterprise production activities. A system of fuzzy predicates was developed to formalize basic knowledge of production and commercial activities related to solving the problems of managing production orders. The applied theoretical methods and practical approaches to solving problems of a qualitative nature are considered in the paper.

AustLII's DataLex Developer's Manual (1st Edition, June 2019)

This Manual is the complete instructions for the use of writing and utilising knowledge-bases using AustLII’s DataLex software. It is intended principally for the coding of legal rules and/or business rules. DataLex uses an English-like knowledge representation to code rules and other constructs. It is based primarily on propositional logic, with the addition of some features similar to first order predicate logic, and others which allow a form of case-based (or example-based) reasoning. The Manual covers the following topics: • DataLex legal knowledge-base systems; • Rule-based inferencing (I): Knowledge-bases and rules; (II): Descriptors, keywords and expressions; (III): Rule types, statements and evaluation order; • Integration of DataLex knowledge-bases with AustLII and other LIIs; • Document assembly using DataLex; • Case-based (example-based) inferencing using DataLex; • DataLex user interface manual. Knowledge-bases (KBs) created with the DataLex software are intended to run in the AustLII Communities environment (the DataLex Community), and to interact with databases on the Australasian Legal Information Institute (AustLII) or other legal information institutes. A publicly accessible DataLex KB Development Tools page allows anyone to develop and test DataLex applications. Access details for the DataLex Community and the KB Development Tools are provided in the Manual, with tutorial instructions for their use.

Applied calculus of fuzzy predicates for the formalization of knowledge

The formalization of knowledge remains one of the main problems of informatization. Special, applied knowledge can be streamlined, brought to a logical level and used to solve specific problems of a qualitative nature. The problems of applied fuzzy knowledge formalization from the point of view of mathematical logic and the theory of fuzzy sets are considered. Use of the applied calculus of fuzzy predicates of the first order was developed and proposed for the representation of knowledge and problem solving. The developed methods were used in the expert system for scientific research in the field of molecular spectroscopy, as well as other subject areas.

О базисах тождеств многообразий группоидов отношений

Множество бинарных отношений, замкнутое относительно некоторой совокупности операций над ними, образует алгебру, называемую алгеброй отношений. Всякую такую алгебру можно рассматривать как упорядоченную отношением теоретико-множественного включения. Для заданного множества Ω операций над бинарными отношениями обозначим через V ar{Ω} [V ar{Ω,⊂}] многообразие, порождённое алгебрами [соответственно упорядоченными алгебрами] отношений с операциями из Ω. Операции над отношениями, как правило, задаются формулами исчисления предикатов первого порядка. Такие операции называются логическими. Важным классом логических операция является класс диофантовых операций. Операция называется диофантовой, если она может быть задана с помощью формулы, которая в своей предваренной нормальной форме содержит лишь операции конъюнкции и кванторы существования. В работе изучаются алгебры отношений с одной бинарной диофантовой операцией, то есть группоиды отношений. В качестве рассматриваемой операции выступает диофантова операция *, определяемая следующим образом: ρ*σ = {( x,у) ∈ X × X : (∃z)( x, z) ∈ ρ∧( x, z) ∈ σ}. Отношение ρ*σ представляет собой результат цилиндрификации пересечения ρ∩σ бинарных отношений ρ и σ. В работе находятся конечные базисы тождеств для многообразий V ar{*} иVar{*,⊂}. Группоид (A, ) принадлежит многообразиюV ar{*} тогда и только тогда, когда он удовлетворяет тождествам: xy = уx (1), (xу)2= xу (2), (xу)у = xу (3), x2у2= x2у (4), (x2у2)z = x2(у2z) (5). Упорядоченный группоид (A,·,≤) принадлежит многообразию V ar{*,⊂} тогда и только тогда, когда он удовлетворяет тождествам (1)–(5) и тождествам: х ≤ x2(6), xу ≤ x2(7). В качестве следствия также получен конечный базис тождеств многообразияVar{*,∪}.

A logic-based framework for collection/item metadata relationships

PurposeThe purpose of this paper is to present a framework for the articulation of relationships between collection-level and item-level metadata as logical inference rules. The framework is intended to allow the systematic generation of relevant propagation rules and to enable the assessment of those rules for particular contexts and the translation of rules into algorithmic processes.Design/methodology/approachThe framework was developed using first order predicate logic. Relationships between collection-level and item-level description are expressed as propagation rules – inference rules where the properties of one entity entail conclusions about another entity in virtue of a particular relationship those individuals bear to each other. Propagation rules for reasoning between the collection and item level are grouped together in the framework according to their logical form as determined by the nature of the propagation action and the attributes involved in the rule.FindingsThe primary findings are the analysis of relationships between collection-level and item-level metadata, and the framework of categories of propagation rules. In order to fully develop the framework, the paper includes an analysis of colloquial metadata records and the collection membership relation that provides a general method for the translation of metadata records into formal knowledge representation languages.Originality/valueThe method for formalizing metadata records described in the paper represents significant progress in the application of knowledge representation techniques to problems of metadata creation and management, providing a flexible technique for encoding colloquial metadata as a set of statements in first-order logic. The framework of rules for collection/item metadata relationships has a range of potential applications for the enhancement or metadata systems and vocabularies.

Asynchronous Arbitrary Pattern Formation: the effects of a rigorous approach

Given any multiset F of points in the Euclidean plane and a set R of robots such that $$|R|=|F|$$ , the Arbitrary Pattern Formation (APF) problem asks for a distributed algorithm that moves robots so as to reach a configuration similar to F. Similarity means that robots must be disposed as F regardless of translations, rotations, reflections, uniform scalings. Initially, each robot occupies a distinct position. When active, a robot operates in standard Look–Compute–Move cycles. Robots are asynchronous, oblivious, anonymous, silent and execute the same distributed algorithm. So far, the problem has been mainly addressed by assuming chirality, that is robots share a common left–right orientation. We are interested in removing such a restriction. While working on the subject, we faced several issues that required close attention. We deeply investigated how such difficulties were overcome in the literature, revealing that crucial arguments for the correctness proof of the existing algorithms have been neglected. The systematic lack of rigorous arguments with respect to necessary conditions required for providing correctness proofs deeply affects the validity as well as the relevance of strategies proposed in the literature. Here we design a new deterministic distributed algorithm that fully characterizes APF showing its equivalence with the well-known Leader Election problem in the asynchronous model without chirality. Our approach is characterized by the use of logical predicates in order to formally describe our algorithm as well as its correctness. In addition to the relevance of our achievements, our techniques might help in revising previous results. In fact, it comes out that well-established results like (Fujinaga et al. in SIAM J Comput 44(3):740–785, 2015), more recent approaches like (Bramas and Tixeuil, in: Proceedings of the 35th ACM SIGACT-SIGOPS symposium on principles of distributed computing (PODC), 2016; Bramas and Tixeuil, in: Proceedings of the 18th international symposium on stabilization, safety, and security of distributed systems (SSS), 2016) and ‘unofficial’ results like (Dieudonne et al., in: CoRR arXiv:0902.2851 , 2009) revealed to be not correct.

Inference algorithm for teams of robots using local interaction

One of the possible approaches to the technical implementation of logical inference in robot groups is considered in paper. The problem is that the usual implementations of the inference mechanism, for example, which are used in expert systems, are difficult to implement to robots that work in a team. It is due to the fragmented knowledge of each robot about the environment where they perform the tasks assigned, the need to exchange data during the inference and monitor this process, etc. In addition, the presence of an inference subsystem may be necessary for emergence of emergent properties in a group of robots. The output subsystem can be used to solve a variety of tasks, for example, choosing the most preferred strategy for the whole collective, building a general picture of the world, planning, etc. In this regard, the paper presents some mechanisms that allow the inference in the logic of predicates of the first order for a team of robots whose interaction with each other is exclusively local in nature. The inference procedure is carried out in the team of robots, which form a special structure, called a static swarm.

The principle of reductio ad absurdum as an ontological problem

The ontological status of evidence is reduced to reducing to absurdity. The problem is that in such evidence, an impossible (or still possible?) Situation is allowed as the initial one. What is the ontological status of such situations, do they have an ontological justification? The answer to this question involves considering the structure of evidence by reducing to absurdity, choosing the appropriate logic and searching for an adequate ontology. The article shows that in the classical calculus of predicates of the first order, proofs by reduction to absurdity are included as a special case of proof by contradiction. The intuitionistic predicate calculus uses evidence to reduce to absurdity, but evidence from the contrary is not accepted in it. Further, the key concept of “absurdity” is discussed. It is shown that the treatment of absurdity as nonsense leads to a dead end, because the problem of meaning does not have an adequate solution in modern science. We can not guarantee the presence of a semantic meaning for correctly constructed expressions of the sign system, but we can ensure the presence of a denotational value for such expressions in artificial sign systems. As applied to our problem, this indicates the need to search for the denotational significance of contradictions. Since the models of logical calculi are constructed by means of set theory, the domain of the search is narrowed to the choice of an appropriate set theory. The modified set theory ZF is considered in which the axiom of the existence of an empty set is replaced by its negation. In this case, it is possible to give the denotational significance to the contradictions, but then the contradictions of the type A and not- A get an ontological justification, since both A and non- A are fulfilled.

Game Semantics in Teaching of Classical First Order Predicate Logic to Stu- dents of Computer Science

Game-theoretical interpretation of logical semantics has been first suggested in 1950s. Although it is well know among professionals, it is often excluded from introductory courses in logic. In this paper we examine whether and to what extent would including game semantics in the syllabus of an introductory course of predicate and propositional logic prove to be beneficial to students’ understanding of the subject. To that purpose, we have exposed two groups of undergraduate students of computer science to game semantics as part of recitations for the course Propositional and Predicate Logic. We focus mainly on how this affects students’ mastery of two particular topics – alternating quantification and restricted quantification. Observations were made during the recitations to evaluate any changes in students’ approach to solving relevant problems in classroom. Moreover, before the final test of the recitations one of the groups was given a brief review of game semantics and the other was not. We have measured the difference in performance of these two groups and the results support the hypothesis that game semantics helps students master certain topics of predicate logic. We reference some of the later research in psychology and pedagogy to help us explain this effect.

All Properties are Divine or God Exists - The Sacred Thesis and its Ontological Argument

A metaphysical system engendered by a third order quantified modal logic S5 plus impredicative comprehension principles is used to isolate a third order predicate D , and by being able to impredicatively take a second order predicate G to hold of an individual just if the individual necessarily has all second order properties which are D we in Section 2 derive the thesis (40) that all properties are D or some individual is G. In Section 3 theorems 1 to 3 suggest a sufficient kinship to Godelian ontological arguments so as to think of thesis (40) in terms of divine property and Godly being; divine replaces positive with Godel and others. Thesis (40), the sacred thesis, supports the ontological argument that God exists because some property is not divine. In Section 4 a fixed point analysis is used as diagnosis so that atheists may settle for the minimal fixed point. Theorem 3 shows it consistent to postulate theistic fixed points, and a monotheistic result follows if one assumes theism and that it is divine to be identical with a deity. Theorem 4 (the Monotheorem) states that if Gg and it is divine to be identical with g , then necessarily all objects which are G are identical with g . The impredicative origin of D suggests weakened Gaunilo-like objections that offer related theses for other second order properties and their associated diverse presumptive individual bearers. Nevertheless, in the last section we finesse these Gaunilo-like objections by adopting what we call an apathiatheistic opinion which suggest that the best concepts `God’ allow thorough indifference as to whether God exists or not.

A novel approach to describing and detecting performance anti-patterns

Anti-pattern, as an extension to pattern, describes a widely used poor solution which can bring negative influence to application systems. Aiming at the shortcomings of the existing anti-pattern descriptions, an anti-pattern description method based on first order predicate is proposed. This method synthesizes anti-pattern forms and symptoms, which makes the description more accurate and has good scalability and versatility as well. In order to improve the accuracy of anti-pattern detection, a Bayesian classification method is applied in validation for detection results, which can reduce false negatives and false positives of anti-pattern detection. Finally, the proposed approach in this paper is applied to a small e-commerce system, the feasibility and effectiveness of the approach is demonstrated further through experiments.

Representing Semantics of Text by Acquiring its Canonical Form

Canonical form is a notion stating that related idea should have the same meaning representation. It is a notion that greatly simplifies task by dealing with a single meaning representation for a wide range of expression. The issue in text representation is to generate a formal approach of capturing meaning or semantics in sentences. These issues include heterogeneity and inconsistency in text. Polysemous, synonymous, morphemes and homonymous word poses serious drawbacks when trying to capture senses in sentences. This calls for a need to capture and represent senses in order to resolve vagueness and improve understanding of senses in documents for knowledge creation purposes. We introduce a simple and straightforward method to capture canonical form of sentences. The proposed method first identifies the canonical forms using the Word Sense Disambiguation (WSD) technique and later applies the First Order Predicate Logic (FOPL) scheme to represent the identified canonical forms. We adopted two algorithms in WSD, which are Lesk and Selectional Preference Restriction. These algorithms concentrate mainly on disambiguating senses in words, phrases and sentences. Also we adopted the First order Predicate Logic scheme to analyse argument predicate in sentences, employing the consequence logic theorem to test for satisfiability, validity and completeness of information in sentences.

Children's comprehension of plural predicate conjunction.

Previous developmental studies of conjunction have focused on the syntax of phrasal and sentential coordination (Lust, 1977; de Villiers, Tager-Flusberg & Hakuta, 1977; Bloom, Lahey, Hood, Lifter & Fiess, 1980, among others). The present study examined the flexibility of children's interpretation of conjunction. Specifically, when two predicates that can apply simultaneously to a single individual are conjoined in the scope of a plural definite (The bears are big and white), conjunction receives a Boolean, intersective interpretation. However, when the conjoined predicates cannot apply simultaneously to an individual (The bears are big and small), conjunction receives a weaker 'split' interpretation (Krifka, 1990; Lasersohn, 1995; Winter, 1996). Our experiments reveal that preschool-aged children are sensitive to both intersective and split interpretations, and can use their lexical and world knowledge of the relevant predicates in order to select an appropriate reading.