A New Approach for Simplification of Logical Propositions with Two Propositional Variables Using Truth Tables

Background: Propositions simplification is a classic topic in discrete mathematics that is applied in different areas of science such as programs development and digital circuits design. Investigating alternative methods would assist in presenting different approaches that can be used to obtain better results. This paper proposes a new method to simplify any logical proposition with two propositional variables without using the logical equivalences. Methods: This method is based on constructing a truth table for the given proposition, and applying one of the following two concepts: the sum of Minterms or the product of Maxterms which has not been used previously in discrete mathematics, along with five new rules that are introduced for the first time in this work. Results: The proposed approach was applied to some examples, where its correctness was verified by applying the logical equivalences method. Applying the two methods showed that the logical equivalences method cannot give the simplest form easily; especially if the proposition cannot be simplified, and it cannot assist in determining whether the obtained solution represent the simplest form of this proposition or not. Conclusion: In comparison with the logical equivalences method, the results of all the tested propositions show that our method is outperforming the current used method, as it provides the simplest form of logical propositions in fewer steps, and it overcomes the limitations of logical equivalences method. Originality/value: This paper fulfils an identified need to provide a new method to simplify any logical proposition with two propositional variables.

Valid Arguments and Heyting Algebra using Multi Valued Logic

Over last three decades, multi valued logic (MVL) has been receiving considerable attention. So, we focus our concentration upon multi valued logic using some of the rules of mathematical logic, which can be used in developing artificial intelligence. Since Aristotle’s logic there were only two propositions. Later it was extended to n-valued logical proposition which is greater than 2, that is popularly known as multi valued logic proposition – they are true, false and unknowns. In this paper we will discuss about multi valued logic with 27- possible using Jaina logic and some of the rules as it gives the best results. In Jaina Logic, indeterminant means something which cannot describe more than one aspect at a time. So, we are going to consider each aspect separately and assign True or False. Then according to the given condition we can either apply min or max condition to get a precise solution.

Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets

Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (<A>, <neutA>, <antiA>), where <A> is an entity (i.e. element, concept, idea, theory, logical proposition, etc.), <antiA> is the opposite of <A>, while <neutA> is the neutral (or indeterminate) between them, i.e., neither <A> nor <antiA> [...]

The Tributary Mode of Production and Justifying Ideologies

In his definition of the tributary mode of production, Eric Wolf proposes that those societies that extract economic surplus through political means generate religious models of the cosmos where supernatural beings provide a metaphor of tribute relations in the human world. As Wolf puts it, “…public power is thus transformed into a problem of private morality." This is a classic Marxist assertion that religion creates false consciousness and motivates people to act against their material interests. Rather than assuming this proposition is correct, anthropological data can be employed to assess it. This chapter evaluates whether a society’s mode of production corresponds to beliefs about the structure of the cosmos using ethnographic data from the eHRAF World Cultures database. Do societies where tribute is extracted by political means have similar justifying ideologies? Conversely, do societies where surplus extraction occurs through kin relations lack such justifying ideologies? My goal is to evaluate Wolf’s intuitively logical proposition with anthropological data. The implications of this evaluation are at the heart of a materialist understanding of causation by empirically evaluating whether material conditions influence ideational beliefs.

PENGGUNAAN KONEKTIF LOGIKA PROPOSISIONAL KOLOM OPINI SURAT KABAR HARIAN PAGI PADANG EKSPRESS (Analisis Isi)

AbstrakPenelitan ini bertujuan untuk mendapat pemahaman yang mendalam tentan penggunaan logika proposisional kolom opini dalam surat kabar harian pagi Padang Ekspress yang meliputi penggunaan kata konektif berupa konjungsi (dan), disjungsi (atau), implikasi (jika-maka), ekuivalen (jika dan hanaya jika), dan negasi (tidak) dalam sebuah kalimat. Penelitian ini adalah penelitian kualitatif dengan metode analisis isi. Data dalam penelitian ini adalah kalimat yang menggunakan kata konektif (dan, atau, jika-maka, jika dan hanya jika, negasi) yang terdapat dalam sebuah tulisan opini dalam surat kabar harian pagi Padang Ekspress. Data yang diperoleh dianalisis melalui tiga tahap, pertama klasifikasi data, kedua analisis dan pembahasan data, dan ketiga kesimpulan atau verifikasi. Berdasarkan hasil analisis dan pembahasan dapat disimpulkan secara keseluruhan, penggunaan kata konektif dalam kolom opini surat kabar harian pagi Padang Ekspress sudah tepat, namun perlu perhatian dalam penggunaan kata konektif dan (konjungsi) dan atau (disjungsi) karena berpotensi menimbulkan keambiguan atau multi makna dalam sebuah kalimat.Kata kunci: logika proposisi, kolom opini, analisis isiAbstractThis research aims to gain a deep understanding of the use of logic propositions opinion coloumn in the daily morning newspaper Padang Ekspress thet includes the use of the word connective form a conjunction (and), disjunction (or), the implications (if-then), equivalen (if and only if), and negation (not) in a sentence. This research is qualitative content analysis method. Data In this study is a sentence that uses the connective words (and, or, if-then, if and only if, negation) contained in an opinion article in a daily morning newspaper Padang Ekspress. The data which was analyzed through three stages, first, clarification of the data, second, analysis and discussion of the data, third, conclusions or verification. Based on the analysis and discussion can be summed up as a whole, the use of the word connective in the opinion column daily morning newspaper Padang Ekspress own right, but it needs attention in the use of the word connective and (conjuction) for potentially ambiguos or systemic many in a sentence.Keywords : logical proposition, opinian columns, content analysis

The Speculative Univocity of Being and Language: From the Verb to Univocity

There are many ways to view the genesis of sense in The Logic of Sense. One way that has been emphasised in the secondary literature is as the emergence of consciousness from the body’s affects.1 There is, however, a more interesting and important genesis at stake beneath this one. If the first genesis takes us from the verb to the logical proposition and empirical consciousness, the second off-piste route goes from the verb to the univocity of being. As Deleuze writes, playing on the literal meaning of the scholastic term univocity2 – one voice (voce) – ‘The univocity of Being signifies that Being is Voice, that it is said.’3

Algorithm for topological design of multi-loop hybrid mechanisms via logical proposition

SUMMARYThis paper introduces the mathematical logical proposition into kinematics and presents a novel method for topological design and representation of mechanisms. The six-value non-classical logical matrix in three orders is proposed to represent spatial basic motions, relations, and selection of moving reference frame. The combinatorial logical sets of mechanisms are built and axiomatized to analyze serial–parallel hybrid mechanisms. In accordance to the logical relations, the mapping between topological arrangement and topological geometry is developed, and algorithm of decomposition synthesis is presented. Furthermore, the higher dimensional topological arrangement of multi-loop hybrid mechanism can be obtained by mapping of higher dimensional geometry. At last, four typical examples are developed to illustrate application of method of logical proposition in topological design of mechanisms. The method is helpful for topological design and analysis of multi-loop hybrid mechanisms.