Ordinary Logic Research Articles

ROBIN GEORGE COLLINGWOOD ON THE LOGIC OF TEXTUAL INTERPRETATION

The interpretation of written texts demands from the reader a certain hermeneutic methodology of reading. In this paper we aim to propose the logic of question and answer constructed by the British philosopher Robin George Collingwood as such an instrument. We seek to demonstrate his thesis through the four objectives we set out in this paper, namely (1) to clarify the context in which the idea of such a logic arises; (2) to what extent it differs from ordinary logic as a discipline; (3) to examine whether Collingwood is a revolutionary in this field; and finally (4) to discuss the principles according to which this logic of question and answer operates. The manner in which we approach these issues is intended to make this paper an illustration for the discussion at hand. The consequences of such an approach are welcome as they are hermeneutical in nature, not only facilitating the interpretation of textual materials, but above all helping the reader in understanding them. Thus, the present study can be of value and is helpful to the reader interested in dealing with a wide range of texts, especially those in the [human] spiritual and social sciences.

A polynomial reduction of forks into logic programs

In this research note we present additional results for an earlier published paper [1]. There, we studied the problem of projective strong equivalence (PSE) of logic programs, that is, checking whether two logic programs (or propositional formulas) have the same behaviour (under the stable model semantics) regardless of a common context and ignoring the effect of local auxiliary atoms. PSE is related to another problem called strongly persistent forgetting that consists in keeping a program's behaviour after removing its auxiliary atoms, something that is known to be not always possible in Answer Set Programming. In [1], we introduced a new connective ‘|’ called fork and proved that, in this extended language, it is always possible to forget auxiliary atoms, but at the price of obtaining a result containing forks. We also proved that forks can be translated back to logic programs introducing new hidden auxiliary atoms, but this translation was exponential in the worst case. In this note we provide a new polynomial translation of arbitrary forks into regular programs that allows us to prove that brave and cautious reasoning with forks has the same complexity as that of ordinary (disjunctive) logic programs and paves the way for an efficient implementation of forks. To this aim, we rely on a pair of new PSE invariance properties.

Differentiated Analysis of the «Insult» Speech Genrebased on Messages from a Social Network Internet Sites

The study of Internet mediated speech communication seems relevant due to the dynamic development of the Internet language, the lack of its codification and legal regulation, duplication of social practices and processes in the virtual environment. The present research is focused on one of the conflicting speech genres (speech acts), which is frequent within Internet communication. Speech actions in the genre of insult in some cases acquire illegal actions and are considered from the standpoint of law enforcement in the practice of forensic linguistics. The novelty of this study lies in the differentiated approach to insults as applied not only to the binary division of its interpretation within the ordinary logic and legal grounds, but also to the study of the distinctive characteristics of this phenomenon in refraction to various legal interpretations (in the criminal, civil, administrative codes). We analyzed written messages of Russian-speaking users of the social network site VKontakte, which were considered through the prism of the provisions of Article 5.61 Insult of the Administrative Code of the Russian Federation. In the course of the study, it was revealed that even within a specialized dataset of messages, perceived by the recipients as insulting messages, the share of messages corresponding to the criterion basis of insult (Article 5.61) is negligible.

Comparisons of performance between quantum-enhanced and classical machine learning algorithms on the IBM Quantum Experience

Machine learning is now widely used almost everywhere, primarily for forecasting. In the broadest sense, the machine learning objective may be summarized as an approximation problem, and the issues solved by various training methods can be reduced to finding the optimal value of an unknown function or restoring a function. At the moment, we have only experimental samples of quantum computers based on classical-quantum logic, when quantum gates are used instead of ordinary logic gates, and probabilistic quantum bits are used instead of deterministic bits. Namely, the probabilistic nature problems that provide for the determination of a certain optimal state from a large set of possible ones on which quantum computers can achieve “quantum supremacy” – an extraordinary (by many orders of magnitude) reduction in the time required to solve the task. The main idea of the work is to identify the possibility of achieving, if not quantum supremacy, then at least a quantum advantage when solving machine learning problems on a quantum computer.

О парадоксальной природе смеха в литературе XX века

The article deals with the attraction of the art of the 20th century to the paradox as a tool for understanding the absurdity of life. Paradox and laughter share their inherent structural ambiguity, pulsating ambivalence. Paradox and laughter are often a platform for the conflict of different logics - ordinary logic and “paralogy” (alogism). Consideration of the typology of objects of ridicule helps to reveal the paradoxical nature of laughter. At the same time, attention is drawn to two types of object: an integral system (institution, professional team, power institutions) and an individual person (in particular, an adventurous hero). It is interesting to study the paradoxical in the very fabric of a comic work. In particular, pleonasm is described as a component of the funny technique. It denotes a paradoxical contradiction between the necessary and the redundant in the description. Paradoxically, the two-dimensional texts associated with the laugh attitude, which are built on the model of the anti-genre, have a conflict-like nature: false panegyrics, anti-idylls, dystopias.

A Critical Examination of the Historical Origins of Connexive Logic

It is often assumed that Aristotle, Boethius, Chrysippus, and other ancient logicians advocated a connexive conception of implication according to which no proposition entails, or is entailed by, its own negation. Thus Aristotle claimed that the proposition ‘if B is not great, B itself is great […] is impossible’. Similarly, Boethius maintained that two implications of the type ‘If p then r’ and ‘If p then not-r’ are incompatible. Furthermore, Chrysippus proclaimed a conditional to be ‘sound when the contradictory of its consequent is incompatible with its antecedent’, a view which, in the opinion of S. McCall, entails the aforementioned theses of Aristotle and Boethius. Now a critical examination of the historical sources shows that the ancient logicians most likely meant their theses as applicable only to ‘normal’ conditionals with antecedents which are not self-contradictory. The corresponding restrictions of Aristotle’s and Boethius’ theses to such self-consistent antecedents, however, turn out to be theorems of ordinary modal logic and thus don’t give rise to any non-classical system of genuinely connexive logic.

CONTROVERSIAL ISSUES OF SUBSUMPTION OF MALFEASANCE

The subject. The article deals with subsumption of malfeasance, judicial characterization of such white-collar crimes.The purpose of the paper is to answer the question of admissibility of qualification of ho-mogeneous actions of a person according to two separate art. 285 and 286 of the Criminal Сode of the Russian Federation.The methodological basis of the research includes general-scientific methods (analysis and synthesis, system-structural approach) as well as academic methods (formal-legal method, method of interpretation of normative legal and judicial acts).Results and scope of application. Within the meaning of paragraph 15 of the Resolution of Plenum of Supreme Court of the Russian Federation, it is absolutely clear that legal actions of an official, which were not caused by official necessity, must be qualified under art. 285 of the Criminal Code of the Russian Federation.Not only legally, but even from the point of view of ordinary logic, the qualification of ho-mogeneous actions by different criminal law norms is unacceptable.Due to the fact that art. 286 of the Criminal Code of the Russian Federation is not a crime of corruption by its characteristics, art. 285 of the Сriminal Сode of the Russian Federation cannot be regarded as a special case of abuse of power.Conclusions. This is unacceptable to qualify the homogeneous actions of a person according to two separate articles – art. 285 and 286 – of the Criminal Сode of the Russian Federation. It is necessary to add the Resolution of Plenum of Russian Supreme Court from October 16, 2009, No. 19 by the provisions more specifically delimiting qualification of malfeasance crimes according to art. 285 and 286 of the Criminal Сode of the Russian Federation.

Parallel distributed compensation for improvement of level control in carbonization column for soda production

The liquid level control is essential in many production installations but the classic approaches often fail to ensure the desired performance. The reasons are the plant nonlinearity, the level oscillations and the plant model uncertainties. The aim of the present investigation is to improve the existing linear control of the level in the carbonization columns for soda ash production by employing fuzzy logic using parallel distributed compensation (PDC). The design of the PDC is based on a nonlinear Takagi–Sugeno–Kang (TSK) plant model which is derived via genetic algorithms optimization and validated using the data from the real time linear level control. The PDC control performs soft blending of the outputs of several parallel local linear controllers each developed for the local linear plant of the TSK model. The fuzzy rules are represented by ordinary logics conditions to enable the PDC programming and use by an industrial programmable logic controller. The PDC increases the dynamic accuracy in the level control and reduces the frequency of the control oscillations compared to the previous linear control thus prolonging the lifetime of the expensive pneumatic actuators used.

Computational Fractal Logic for Quantum Physics and Cosmology

In the spirit of the work of Ramanujan’s infinite Cesaro sum and the formalization of his work by G. Hardy, we propose that quantum physics and cosmology are governed by fractal logic rather than ordinary classical logic. Various general considerations as well as specific examples are given to illustrate and support our thesis leading to a revision of the standard model of elementary particles as well as relativity. These examples range from the practical aspect to almost esoteric considerations but at the end, everything converges towards a unity of theory and computation presented in the form of modern fractal logic and transfinite quantum field theory in a Cantorian spacetime. We conclude that the universe is akin to a transfinite Turing machine, or a Transfinite Infinite capacity of 'tHooft Automaton.

On a Dialogical Point of View of Matrices

La logique dialogique ordinaire propose un traitement de la mémoire sous la forme d'un historique des dialogues. Rechercher une référence (la justification) dans cet historique est un processus ambiguë en cas de répétition, ce qui peut rendre complexes ou impossibles les questions de composition de dialogue. Ainsi, deux recherches de justification peuvent se superposer en une double justification problématique. De plus, ce traitement de la mémoire coûte techniquement beaucoup de ressources.Nous proposons un formalisme de la dialogique qui résout ces problèmes: double-justification, composition, économie de mémoire. Pour ce faire, nous internaliserons des règles analysées comme "spéciales", reconfigurant en grande partie le formalisme et à sa suite les notions philosophiques voire métaphysiques mises en jeu dans ce système logique et dans ses interprétations.Cet article se découpe en trois parties :Une présentation du cadre dialogique orientée vers la présentation du problème de la double justification.Une ré-interprétation de ce cadre en termes de matrices : les formules logiques calquées sur la lecture linguistico-mathématique du langage sont remplacées par un concept emprunté à la game semantic, celui de position (sous la forme de matrices de formules).Une brève synthèse des nouvelles perspectives offertes par cette méthode : réaffirmation de la séparation claire entre les différents niveaux d'analyse et économie sur la quantité de mémoire requise (payée en complexité).

필요조건, 충분조건 개념의 학습과 관련한 문제들

The reason of the confusion of learners about the logic concepts such as implication, necessary condition and sufficient condition can be analyzed from the point of view of history of logic, discrepancy between ordinary language and formal logic, and reification which occurs in the process of cognition of discursive object and also indicates the necessity of a research. This study analysed the difficulties related to study and implication concept and attempted to the reflection of textbook and curriculum. Not that ordinary language makes the introduction of formal language easier, but that this study discussed the possibilities ordinary language intervenes the learning of formal language. This study additionally intended to understand learning difficulties of concrete subjects, abstract subjects and the gap between primary object and discursive object by understanding the process of sagging, encapsulating and reifying.

Verifying specifications with associated attributes in graph transformation systems

Graph transformation is an important modeling and analysis technique widely applied in software engineering. The attributes can naturally conceptualize the properties of the modeled artifacts. However, the lack of support for the specification of such attribute correspondence by ordinary propositional temporal logics hampers its further application during verification. Different from the theoretical investigations on quantified second order logics, we propose a practical and light-weight approach for the verification of this kind of temporal specifications with associated attributes. Particularly, we apply our approach and extend the generalpurpose graph transformation modeling tool: Groove. Moreover, symmetry reduction techniques are exploited to reduce the number of states. Experiments with performance evaluations complement our discussion and demonstrate the feasibility and efficiency of our approach.

Predicate Logic with Anaphora

In this paper I make a case for a separate treatment of (singular) anaphoric pronouns within a predicate logic with anaphora (PLA). Discourse representation theoretic results (from Kamp 1981) can be formulated in a compositional way, without fid­dling with orthodox notions of scope and binding. In contrast with its predecessor dynamic predicate logic (Groenendijk and Stokhof 1991), the system of PLA is a proper extension of ordinary predicate logic and it has a genuine update semantics. Moreover, in contrast with other compositional reformulations of DRT, the seman­tics of PLA remains well within the bounds of ordinary, extensional type theory.

”När det tar slut och börjar om igen”: Ekokritiska perspektiv på Stefan Castas ungdomsdystopier

The Swedish author Stefan Casta has written several books for children and adults, thematically addressing nature and environment. This paper highlights and discusses ideological and aesthetical aspects in his recent novel, Den gröna cirkeln (2011) and its sequel, Under tiden (2012), from an ecocritical perspective. The novels combine environmental commitment with a dystopian story about four young people who survive a climate catastrophe but get lost in a world they no longer recognize and where ordinary logic does not seem to exist. The paper elucidates this process by a comparison with Buell’s (2001) concept of toxic discourse as there are several parallells, such as elements like a lost paradise, inescapable toxic, and the oppression of powerful societal interests, throughout the story. Simultaneously, ambivalence towards culture and civilization is expressed. Nature and culture become intertwined in a way that differs from the conventional dichotomy and this complexity is the supporting structure of the texts. The four teenagers, and even more so the following generation, become symbols of a new future, a pattern recognized from much dystopian as well as children’s fiction, where the weak and oppressed turn out to be the heroes. The optimistic and didactic ambition in this kind of dystopian stories is often aimed at creating an engagement for environmental issues and a sustainable future among young people. By placing the story in an imagined future as well as adding fantastic elements, Stefan Casta creates a kind of ”Verfremdungseffekt” on phenomena we often do not question in our lifestyle. This could be a liberating relativization to the young readers; the social and cultural drives that rule many of our life choices are not essential and can therefore always be reconsidered. Keywords: Ecocriticism, Stefan Casta, dystopian fiction, nature, environment, climate change

Optimization, Modeling, and Online Monitoring of the Enzymatic Extraction of Banana Juice

This article focuses on the optimization, modeling, and online monitoring of banana juice production through an enzymatic method. In order to perform this task, a batch reactor was designed with automatic control over the temperature and the agitation speed as well as online monitoring of torque. The experiments were carried out with the Musa AAA Cavendish banana variety (Enano gigante), the main variety planted in Mexico. Three different ripening stages were evaluated. Optimization of juice extraction was evaluated as a function of the pulp/water relationship and the concentration of the enzyme complex. The results showed that the adding of water had no influence on the extraction of banana juice, and the optimal enzyme concentration per kilogram of banana pulp was found. Based on a fuzzy logic approach, it was possible to relate the initial torque with the ripeness stage. Furthermore, an observable dynamical model based on ordinary differential equations and fuzzy logic is presented. With this model, the relationship between the torque dynamic and the instant juice yield was found to depend on the amount of enzyme, the temperature, and the maturity stage of the banana used. In addition, a principal components analysis was used to classify and to relate the final juice characteristics (e.g., L, a, and b colorimetric components) to the processing conditions and the final appreciation of a group of sensorial panelists. Additionally, a robust observer was designed and implemented to filter the noise present in the torque signal and to predict the instant juice yield.

Which Mathematical Logic is the Logic of Mathematics?

The main tool of the arithmetization and logization of analysis in the history of nineteenth century mathematics was an informal logic of quantifiers in the guise of the “epsilon–delta” technique. Mathematicians slowly worked out the problems encountered in using it, but logicians from Frege on did not understand it let alone formalize it, and instead used an unnecessarily poor logic of quantifiers, viz. the traditional, first-order logic. This logic does not e.g. allow the definition and study of mathematicians’ uniformity concepts important in analysis. Mathematicians’ stronger logic was rediscovered around 1990 as the form of independence-friendly logic which hence is not a new logic nor a further development of ordinary first-order logic but a richer version of it.

How many notions of necessity?

Evans distinguishes between superficial necessity and deep necessity in his analysis of the contingent a priori. The distinction between these two notions of necessity is formalized by Davies and Humberstone through the addition of the operator Fixedly to Actuality Modal Logic (AML, S5A), where deep necessity is represented by the combination Fixedly Actually. Wehmeier’s Subjunctive Modal Logic (SML) provides an extension of the expressive capacity of ordinary modal predicate logic alternative to AML. I add Fixedly to SML and show that in the system SML with Fixedly the distinction between deep and superficial necessity disappears. I conclude that the existence of the distinction between deep and superficial necessity, as well as the existence of the contingent a priori, cannot be asserted independently of the choice of background logic.

Well-founded semantics for description logic programs in the semantic web

The realization of the Semantic Web vision, in which computational logic has a prominent role, has stimulated a lot of research on combining rules and ontologies, which are formulated in different formalisms. In particular, combining logic programming with the Web Ontology Language (OWL), which is a standard based on description logics, emerged as an important issue for linking the Rules and Ontology Layers of the Semantic Web. Nonmonotonic description logic programs (dl-programs) were introduced for such a combination, in which a pair(L,P)of a description logic knowledge baseLand a set of rulesPwith negation as failure is given a model-based semantics that generalizes the answer set semantics of logic programs. In this article, we reconsider dl-programs and present a well-founded semantics for them as an analog for the other main semantics of logic programs. It generalizes the canonical definition of the well-founded semantics based on unfounded sets, and, as we show, lifts many of the well-known properties from ordinary logic programs to dl-programs. Among these properties, our semantics amounts to a partial model approximating the answer set semantics, which yields for positive and stratified dl-programs, a total model coinciding with the answer set semantics; it has polynomial data complexity provided the access to the description logic knowledge base is polynomial; under suitable restrictions, it has lower complexity and even first-order rewritability is achievable. The results add to previous evidence that dl-programs are a versatile and robust combination approach, which moreover is implementable using legacy engines.

The Obscene and the Corpse

This paper examines Jean-Michel Basquiat’s obsession with the marginal and the obscene - understood literally as the ob-scene. The context of a graffiti art, and particularly the glyphic character of graffiti art, allows the work to defy the ordinary logic of the picture frame in order to figure, rather than represent, indeterminate into it. Thus, Basquiat characterizes death and the dead body not in the light of a transcendent space but as prolonged into the depths of an alterity, an ob-scene in the sense of an alter-side that belongs to the scene.

A Short Note on the Logico-Conceptual Foundations of Information Theory in Partition Logic

A new logic of partitions has been developed that is dual to ordinary logic when the latter is interpreted as the logic of subsets of a fixed universe rather than the logic of propositions. For a finite universe, the logic of subsets gave rise to finite probability theory by assigning to each subset its relative size as a probability. The analogous construction for the dual logic of partitions gives rise to a notion of logical entropy that is precisely related to Claude Shannon's entropy. In this manner, the new logic of partitions provides a logico-conceptual foundation for information-theoretic entropy or information content.