scholarly journals Catatan Awal tentang Logika Sentensial dan implikasinya dalam diskusi Manunggaling Kawula Gusti dan Trinitas

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Victor Christianto

AbstrakDalam catatan awal ini kami mengajukan argumen bahwa konsep logikasentensial memuat kemungkinan betweenness/neitherness/ bothness yang tidakdikenal dalam logika biner Aristotelian. Kami mengusulkan bahwa konsep logikasentensial akan berguna untuk menjembatani dialog antara pendukung nondualisme seperti mistisisme kaum sufi dan para pendukung mazhab dualisme.Dalam konteks ini, kekristenan menawarkan kerangka berpikir bahwa hanyaYesuslah satu-satunya Sang Manunggaling Kawula Gusti yang sejati, sementarakita sebagai manusia dapat berperan sekaligus sebagai makhluk yang berbedadengan Sang Gusti, namun pada saat yang sama, umat percaya menyatu denganTuhan, meski bukan dengan konsep manunggalnya para sufi. Artinya, logikasentensial/ proposisional memungkinkan kita memahami bahwa manusiaserempak disatukan dengan Sang Khalik, namun pada saat yang sama tetapberbeda dengan Sang Khalik. Artinya non-dualisme dan dualisme pada saat yangsama. Tentunya diperlukan kajian yang lebih mendalam mengenai topik ini, yangakan kami tuliskan dalam artikel lain kemudian. AbstractIn this introductory exploration, we argue that the concept of sentential logiccontains a possibility of betweenness / neitherness / bothness unknown toAristotelian binary logic. We propose that the concept of sentential logic will beuseful for bridging the dialogue between supporters of non-dualism such as themysticism of the Sufis and the supporters of the dualism schools. In this context,Christianity offers a framework of thinking that only Jesus is the trueManunggaling Kawula Gusti, while we humans can simultaneously act ascreatures that are different from the Gusti (God), but at the same time, believersare one with God, although not the same with the concept of divine unity of theSufis. That is, sentential / propositional logic makes it possible that humans aresimultaneously united with the Creator, but at the same time remain differentfrom the Creator. It means non-dualism and dualism at the same time. For sure, amore in-depth exploration is required, and we plan to present it in another article.

2019 ◽  
Author(s):  
Matheus Pereira Lobo

All nine axioms and a single inference rule of logic (Modus Ponens) within the Hilbert axiomatic system are presented using capital letters (ABC) in order to familiarize the beginner student in hers/his first contact with the topic.


2003 ◽  
Author(s):  
Ofer Strichman ◽  
Sanjit A. Seshia ◽  
Randal E. Bryant
Keyword(s):  

2020 ◽  
Author(s):  
Michał Walicki

Abstract Graph normal form, introduced earlier for propositional logic, is shown to be a normal form also for first-order logic. It allows to view syntax of theories as digraphs, while their semantics as kernels of these digraphs. Graphs are particularly well suited for studying circularity, and we provide some general means for verifying that circular or apparently circular extensions are conservative. Traditional syntactic means of ensuring conservativity, like definitional extensions or positive occurrences guaranteeing exsitence of fixed points, emerge as special cases.


Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1456
Author(s):  
Stefka Fidanova ◽  
Krassimir Todorov Atanassov

Some of industrial and real life problems are difficult to be solved by traditional methods, because they need exponential number of calculations. As an example, we can mention decision-making problems. They can be defined as optimization problems. Ant Colony Optimization (ACO) is between the best methods, that solves combinatorial optimization problems. The method mimics behavior of the ants in the nature, when they look for a food. One of the algorithm parameters is called pheromone, and it is updated every iteration according quality of the achieved solutions. The intuitionistic fuzzy (propositional) logic was introduced as an extension of Zadeh’s fuzzy logic. In it, each proposition is estimated by two values: degree of validity and degree of non-validity. In this paper, we propose two variants of intuitionistic fuzzy pheromone updating. We apply our ideas on Multiple-Constraint Knapsack Problem (MKP) and compare achieved results with traditional ACO.


Axioms ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. 115 ◽  
Author(s):  
Joanna Golińska-Pilarek ◽  
Magdalena Welle

We study deduction systems for the weakest, extensional and two-valued non-Fregean propositional logic SCI . The language of SCI is obtained by expanding the language of classical propositional logic with a new binary connective ≡ that expresses the identity of two statements; that is, it connects two statements and forms a new one, which is true whenever the semantic correlates of the arguments are the same. On the formal side, SCI is an extension of classical propositional logic with axioms characterizing the identity connective, postulating that identity must be an equivalence and obey an extensionality principle. First, we present and discuss two types of systems for SCI known from the literature, namely sequent calculus and a dual tableau-like system. Then, we present a new dual tableau system for SCI and prove its soundness and completeness. Finally, we discuss and compare the systems presented in the paper.


2010 ◽  
Vol 3 (1) ◽  
pp. 41-70 ◽  
Author(s):  
ROGER D. MADDUX

Sound and complete semantics for classical propositional logic can be obtained by interpreting sentences as sets. Replacing sets with commuting dense binary relations produces an interpretation that turns out to be sound but not complete for R. Adding transitivity yields sound and complete semantics for RM, because all normal Sugihara matrices are representable as algebras of binary relations.


2013 ◽  
Vol 70 (3) ◽  
pp. 279-312
Author(s):  
Rosa Camps ◽  
Xavier Mora ◽  
Laia Saumell

2006 ◽  
Vol 45 (1) ◽  
pp. 228-261 ◽  
Author(s):  
Graciela Domenech ◽  
Hector Freytes
Keyword(s):  

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