scholarly journals APPLICATION OF ALGORITHMIC ALGEBRA SYSTEM FOR GRAMMATICAL ANALYSIS OF SYMBOLIC COMPUTATION EXPRESSIONS OF PROPOSITIONAL LOGIC

Author(s):  
V. V. Lytvyn ◽  
I. O. Bobyk ◽  
V. A. Vysotska
Author(s):  
Paul Smolensky ◽  
Eric Rosen ◽  
Matthew Goldrick

In certain French words, an orthgraphically-final consonant is unpronounced except, in certain environments, when it precedes a vowel. This phenomenon, liaison, shows significant interactions with several other patterns in French (including h-aspiré, schwa deletion, and the presence of other morphemes in the liaison context). We present a learning algorithm that acquires a grammar that accounts for these patterns and their interactions. The learned grammar employs Gradient Symbolic Computation (GSC), incorporating weighted constraints and partially-activated symbolic representations. Grammatical analysis in the GSC framework includes the challenging determination of the numerical strength of symbolic constituent activations (as well as constraints). Here we present the first general algorithm for learning these quantities from empirical examples: the Error-Driven Gradient Activation Readjustment (EDGAR). Smolensky and Goldrick (2016) proposed a GSC analysis, with hand-determined numerical strengths, in which liaison derives from the coalescence of partially-activated input consonants. EDGAR allows us to extend this work to a wider range of liaison phenomena by automatically determining the more comprehensive set of numerical strengths required to generate the complex pattern of overall liaison behaviour.


10.2514/3.920 ◽  
1997 ◽  
Vol 11 ◽  
pp. 472-476
Author(s):  
Henry H. Kerr ◽  
F. C. Frank ◽  
Jae-Woo Lee ◽  
W. H. Mason ◽  
Ching-Yu Yang

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):  

Author(s):  
Jessica Keiser

In Imagination and Convention: Distinguishing Grammar and Inference in Language, Ernie Lepore and Matthew Stone offer a multifaceted critique of the Gricean picture of language use, proposing in its place a novel framework for understanding the role of convention in linguistic communication. They criticize Lewis’s and Grice’s commitment to what they call ‘prospective intentionalism,’ according to which utterance meaning is determined by the conversational effects intended by the speaker. Instead, they make a case for what they call ‘direct intentionalism’, according to which utterance meaning is determined by the speaker’s intentions to use it under a certain grammatical analysis. I argue that there is an equivocation behind their critique, both regarding the type of meaning that is at issue and the question each theory is attempting to answer; once we prise these issues apart, we find that Lepore and Stone’s main contentions are compatible with the broadly Lewisian/Gricean picture.


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.


2020 ◽  
Vol 138 (4) ◽  
pp. 618-648
Author(s):  
Rachel A. Burns

AbstractThis article reassesses the grammatically problematic half-line prologa prima (l. 89a) in the Old English wisdom poem Solomon and Saturn I, and suggests that it ought to be emended to the grammatically viable reading of “prologa prim”. Line 89 a introduces a passage in which the words of the Pater Noster become anthropomorphised as warriors and attack the devil. I will argue that “prologa prim” is an exegetical exercise, informed by grammatical theory and liturgical practice, designed for an audience of monastic readers. This multivalent half-line offers different levels of meaning when read according to different permutations of language and metaphor, in a process analogous to the interpretation of scripture according to the influential model of fourfold exegesis. When read literally, as ‘the first of the initial letters’, “prologa prim” indicates the unfolding and time-bound process of reading. Previous scholars (Anlezark 2009; Anderson 1998) have noted the allusive references in line 89 a to Greek logos (‘word’) and Old English prim (‘first hour’, ‘Prime office’), but not their full significance. Through these allusions, the reader shifts from a literal reading to a spiritual and metaphorical reading of the half-line, achieving a diachronic perspective of the Pater Noster’s recitation across time, and finally an atemporal perspective, reading in line 89 a a paraphrase of John 1:1, “In the beginning was the Word”. In conjunction with the subsequent episode of the battle, line 89 a forms an exemplum of the monastic practice of lectio divina. This example of ‘monastic poetics’ (O’Camb 2014; Niles 2019) moves from grammatical analysis to a vision of the Word.


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