Pure Logic Research Articles

Design and Implementation of Adaptive Neuro-fuzzy Exergame Controller

Introduction: Due to sedentary postures caused by video games, many health-related issues have occurred among players. One practical solution for dealing with the aforementioned problem is to come up with game controllers which promote physical exercises. In this study, an adaptive neuro-fuzzy exergame controller was introduced. Materials and Methods: During the training stage, the parameters of the fuzzy logic’s member functions were fine-tuned. By calculating a gradient vector and by applying backpropagation, the aforementioned parameters were updated using the measured error. The controller was made of four pads, each containing a resistor and a pushbutton, which were connected to a microcontroller. In order to improve the user experience, an adaptive neuro-fuzzy logic system was used to analyze the gathered data from the controller. Results: A pure fuzzy logic system (FLS) cannot provide an acceptable playing experience for players of different ages and physical characteristics. The received signal from the controller was sent to a fine-tuned FLS. The calculated output of the previously trained FLS was one of the defined classes of “ignore”, “press”, and “hold”, which was sent as a command to the main computer. Conclusion: In the proposed method, the FLS was fine-tuned by gathering data from the user, which improved the performance of the controller due to the fact that the controller was trained to best suit the needs of the user. The gathered data was then used to change the parameters of the FLS to provide an acceptable playing experience for the user.

Слезы сильнее логики:персонализм Альберта Соболева

The article is devoted to the analysis of the Albert Sobolev’s Personalism. Albert Sobolev (1936‒2019) is the Historian of Russian Philosophy, but he was the original thinker too. The author consider the Sobolev’s personalistic Weltan­schauung using the Sobolev’s intellectual heritage and personal remembrances concerning the life and philosophical activity of his friend. The Sobolev’s philo­sophical opinions were influenced by famous Russian thinkers of Silver Age as Semen L. Frank, Pavel A. Florensky and some others. The author tries to recon­struct the social and cultural context of the spiritual and artistic development of his hero. One of the author’s aim is showing the significance of the philoso­phical dialogue between Sobolev and his friend and constant opponent Sergey M. Polovinkin (1935‒2018), the famous researcher of Russian Philosophy too. The chief Sobolev’s affirmation is that the spiritual and the emotional human state is more important in the philosophical creation than the pure logic. Accord­ing to the author of the article, Sobolev’s personalism characterized by empha­sized culture-centrism and should be designated as Christian spiritualism in on­tology, intuitionism with an apophatic approach in epistemology, and artistry in the style and technique of cognizing thought. Such principles cannot but lead to the requirements of musicality and indirectness of philosophical speech as guarantors of its depth and productivity.

Reality, fundamentality, grounding (and cognate notions)

The notion of grounding is one of the central notions in the debates concerning ontological dependence in contemporary metaphysics and metametaphysics. In this paper we have carried out a comparative analysis of grounding, supervenience, reality, fundamentality, and cognate notions, and we have demonstrated what their role should be in the context of neo-Aristotelian hierarchical ontologies and the project of metaphysical foundationalism. We have also sketched out some basic outlines of what Kit Fine calls ?the pure logic of ground? by establishing certain formal desiderata which grounding ought to meet in order to successfully carry out its specific ontologico- explanatory role. It is finally shown that grounding suffers from similar problems and shortcomings as supervenience, and that a satisfactory solution of those problems cannot be found by looking to metaphysical primitivism according to which grounding is a sui generis, primitive and unanalysable notion which is nonetheless essential for metaphysics. Even though grounding might turn out to be an ?essentially contested concept?, in the end we suggest how the aforementioned problems might be met by means of holistic considerations of grounding within the broader context of the entire (meta)metaphysical theory.

A Novel Method of Evidential Network Reasoning Based on the Logical Reasoning Rules and Conflict Measure

Evidential reasoning satisfies a weaker condition than probability theory and can deal with uncertain scenarios. However, there is still no complete and consistent theoretical system in the evidential reasoning now. In this paper, a novel method of evidential network reasoning based on the logical reasoning rules and conflict measure is proposed. The state of nodes is described through several basic probability assignments(BPAs). Two logical reasoning rules are defined to show that the occurrence of some antecedents in the parent nodes will lead to the sub-BPAs of the child node occurrence. Then the occurrence probability of sub-BPA with the child node is computed through antecedent probabilities in the parent nodes. Besides, the support degree of sub-BPAs is computed based on the evidential distance. The final BPA of the child node is obtained by combining weighted sub-BPAs. Two examples about fault diagnosis and threat assessment and prediction are given respectively to illustrate the effectiveness of the proposed method. Different from the previous work, this paper defines a new reasoning rule called OR rule, and the computation based on pure logic makes the reasoning process more intuitive. Besides, the weights of sub-BPAs are computed considering both the occurrence probability and conflict measure.

Physical Indeterminacy in Digital Computation

[Church 1931] and [Turing 1936] developed equivalent models of computation based on the concept of an algorithm, which by definition is provided an input from which it is to compute a value without external interaction. After physical computers were constructed, they soon diverged from computing only algorithms meaning that the Church/Turing theory of computation no longer applied to computation in practice because computer systems are highly interactive as they compute, which inspired the development of the Actor Model in 1972 to characterize all digital computation. Indeterminate computation can be thousands of times faster than the parallel λ-calculus (cf. [Takahashi 1989]) or pure logic programs [Hewitt 1969]. This article presents metatheory for a universal theory of digital computation that is more general and powerful than Church/Turing computation [Church 1935, Turing 1936]. Meta[Actors] (meta theory of Actors) proves that theory Actors has the following properties: • The theory Actors is uniquely categorical, i.e., it characterizes Actors (including types) up to an unique isomorphism. • The theory Actors is model sound, i.e., every theorem of Actors of is true in the unique up to isomorphism model. • The unique up to isomorphism model has partial predicates and propositions because of indeterminacy. • Proof checking in the theory Actors is computationally decidable. • There are no “monsters” [Lakatos 1976] in models of the theory Actors such as the ones in 1st-order theories of computation in which there can be Zeno-like computations, which have an infinite number of computational steps between two steps. Consequently unlike 1st-order theories, the theory Actors is not subject to cyberattacks using “monsters” in models. • The theory Actors is algorithmically inexhaustible, i.e., it is impossible to computationally enumerate theorems of the theory thereby reinforcing the intuition behind [Franzen, 2004]. Contrary to [Church 1934], the conclusion in this article is to abandon the assumption that theorems of a theory must be computationally enumerable while retaining the requirement that proof checking must be computationally decidable. Thesis: Any digital system can be directly modeled and implemented using Actors.

Multiple Realizability and Biological Modality

Critics of multiple realizability have recently argued that we should concentrate solely on actual here-and-now realizations that are found in nature. The possibility of alternative, but unactualized, realizations is regarded as uninteresting because it is taken to be a question of pure logic or an unverifiable scenario of science fiction. However, in the biological context only a contingent set of realizations is actualized. Drawing on recent work on the theory of neutral biological spaces, the article shows that we can have ways of assessing the modal dimension of multiple realizability that do not have to rely on mere conceivability.

Absorbing the structural rules in the sequent calculus with additional atomic rules

We show that if the structural rules are admissible over a set $$\mathcal{R}$$ of atomic rules, then they are admissible in the sequent calculus obtained by adding the rules in $$\mathcal{R}$$ to the multisuccedent minimal and intuitionistic $$\mathbf{G3}$$ calculi as well as to the classical one. Two applications to pure logic and to the sequent calculus with equality are presented.

Introducing article numbering to Annals of Pure and Applied Logic

Introducing article numbering to Annals of Pure and Applied Logic

Intuitionistic ancestral logic

Abstract In this article we define pure intuitionistic Ancestral Logic ( iAL ), extending pure intuitionistic First-Order Logic ( iFOL ). This logic is a dependently typed abstract programming language with computational functionality beyond iFOL given by its realizer for the transitive closure, TC . We derive this operator from the natural type theoretic definition of TC using intersection. We show that provable formulas in iAL are uniformly realizable, thus iAL is sound with respect to constructive type theory. We further show that iAL subsumes Kleene Algebras with tests and thus serves as a natural programming logic for proving properties of program schemes. We also extract schemes from proofs that iAL specifications are solvable.

How Misesian Was the Hayekian Research Program?

Hayek often said that his 1937 paper – “Economics and Knowl- edge” -- was a subtle rebuke of Mises’s apriorism. Not, as many might want to believe, in some root and branch fashion, but in the realm of applied theory of which the study of the market economy is to be included. The realm of pure theory – or what Hayek calls the “Pure Logic of Choice” or in other places he calls “The Eco- nomic Calculus” – the essential building block of economic analy- sis reflects the Misesian (or actually Mengerian) position, and more or less the epistemological status of the pure theory aspect of praxeology is upheld by Hayek. As he put it in a much later essay, there is a “Primacy of the Abstract.” And, one must always remem- ber that Mises’s claim is not that he was unique in this endeavor either. As he put it:
 “In asserting the a priori character of praxeology we are not drafting a plan for a future new science different from the tradi- tional sciences of human action. We do not maintain that the theo- retical science of human action should be aprioristic, but that this it is, and always has been so.” (1949, 40)
 I believe the most scientifically productive reading of Hayek’s 1937 paper is as a clarification of the Misesian project with respect to the study of the market economy – or what both Mises and Hayek called “catallactics”. And, in catallactics the pure logic of choice is a necessary component, but not a sufficient one for a full explana- tion. We must, in our quest for a full explanation explore how alter- native institutional arrangements impact the learning of individuals within that system. In this way we move from the pure logic of choice to the situational logic of organizations to the study of the exchange order, and with that productive specialization, peaceful social cooperation, and the entrepreneurial function as an agent of change. This is how I would read the passages in Hayek (1937, 34ff) where he argues that the pure logic of choice is not directly applicable to the explanation of social relations. Equilib- rium for individual choosers, in other words, is quite different from equilibrium achieved by dispersed and diverse individuals. The first is a necessary part of the explanation, but to achieve the sort of dovetailing of plans that defines the equilibrium state in the social relations of the market we must be able to explore how “under certain conditions, the knowledge and intentions of the different members of society are supposed to come more and more into agreement, or, to put the same thing in less general and less exact but more concrete terms, that the expectations of the people and particularly of the entrepreneurs will become more and more correct.” (1937, 45)
 It is in this manner that economics, Hayek argues, ceases to become purely an exercise in pure logic, and becomes in a sense an empirical science.3 It is in the study of how alternative institutional environments influence the behavior of individuals and how that in turn impacts the ability of these individuals to realize the gains from social cooperation under the division of labor. And the behav- ior we must focus our analytical attention on, is how they acquire and utilize the knowledge dispersed throughout the system, in other words how they learn how best to orient their actions with others so as to achieve a coordination of plans that defines the equilibrium of the system.

Muito além do consumo de pão: condições de vida no Rio de Janeiro na década de 1870

Resumo O artigo apresenta, lançando mão de diversas fontes - jornais de época, inventários post-mortem, lista de qualificação de votantes, romances -, as condições de vida dos trabalhadores da Corte, com o objetivo de mostrar que, apesar das inúmeras dificuldades, havia uma margem para consumo de supérfluos e mesmo de acumulação de bens, e que suas escolhas no mercado não são fruto apenas de uma lógica econômica, mas, como argumentou Giovani Levi, refletem também aspectos importantes da cultura desses grupos.

Burali-Forti as a Purely Logical Paradox

Russell’s paradox is purely logical in the following sense: a contradiction can be formally deduced from the proposition that there is a set of all non-self-membered sets, in pure first-order logic—the first-order logical form of this proposition is inconsistent. This explains why Russell’s paradox is portable—why versions of the paradox arise in contexts unrelated to set theory, from propositions with the same logical form as the claim that there is a set of all non-self-membered sets. Burali-Forti’s paradox, like Russell’s paradox, is portable. I offer the following explanation for this fact: Burali-Forti’s paradox, like Russell’s, is purely logical. Concretely, I show that if we enrich the language $\mathcal {L}$ of first-order logic with a well-foundedness quantifier W and adopt certain minimal inference rules for this quantifier, then a contradiction can be formally deduced from the proposition that there is a greatest ordinal. Moreover, a proposition with the same logical form as the claim that there is a greatest ordinal can be found at the heart of several other paradoxes that resemble Burali-Forti’s. The reductio of Burali-Forti can be repeated verbatim to establish the inconsistency of these other propositions. Hence, the portability of the Burali-Forti’s paradox is explained in the same way as the portability of Russell’s: both paradoxes involve an inconsistent logical form—Russell’s involves an inconsistent form expressible in $\mathcal {L}$ and Burali-Forti’s involves an inconsistent form expressible in $\mathcal {L} + \mathsf {W}$ .

Making and Unmaking (Im)Possible Worlds: Language Games, Naming, and Necessities in "The Real Thing"

This article reads "The Real Thing" as a text about the process of naming and the logical function of proper names. Moving from Frege's and Wittgenstein's considerations on sense and reference, the article turns to Saul Kripke's Name and Necessity in order to understand James's strategic use of the name "Monarch" in the story's signifying structure, with reference to the philosopher's theory of the possible worlds. Though foregrounding and anticipating the logical functioning of language in the processes of signification and reference, "The Real Thing" nonetheless signals the need, in order to produce knowledge, to shift from the domain of pure logic to that of epistemology.

Rule-Generation Theorem and its Applications

In several applications of sequent calculi going beyond pure logic, an introduction of suitably defined rules seems to be more profitable than addition of extra axiomatic sequents. A program of formalization of mathematical theories via rules of special sort was developed successfully by Negri and von Plato. In this paper a general theorem on possible ways of transforming axiomatic sequents into rules in sequent calculi is proved. We discuss its possible applications and provide some case studies for illustration.

An elucidating proof that a matched filter is optimum

A matched filter is an essential element in digital communications receivers. It is known that it is optimal, in the sense of producing sufficient statistics of maximum signal-to-noise ratio; a proof is presented in many undergraduate textbooks. Recent research in mathematics education suggests that the purpose of a proof is not merely to convince students that a theorem is true by pure logic; rather, a proof should be explanatory, with semantic content that elucidates the relationship between the concepts involved. In this paper, a time-domain proof that the matched filter is optimal is presented, and it is argued that it has larger explanatory value than alternative proofs.

Information-gain computation in the Fifth system

Despite large incentives, correctness in software remains an elusive goal. Declarative programming techniques, where algorithms are derived from a specification of the desired behavior, offer hope to address this problem, since there is a combinatorial reduction in complexity in programming in terms of specifications instead of algorithms, and arbitrary desired properties can be expressed and enforced in specifications directly.However, limitations on performance have prevented programming with declarative specifications from becoming a mainstream technique for general-purpose programming, because a strategy which is both efficient and fully general to derive algorithms from specifications does not yet exist. To address this bottleneck, I propose information-gain computation, a framework where an adaptive evaluation strategy is used to efficiently perform a search which derives algorithms that provide information about a query via the most efficient routes. Within this framework, opportunities to compress the search space present themselves, which suggest that information-theoretic bounds on the performance of such a system might be articulated and a system might be designed to achieve them. The computation of the information measures that are the basis of this strategy crucially depends on a probabilistic semantics for the relations represented by predicates, which may either already be present in a probabilistic logic language, or may be superimposed on a pure logic language.I describe a prototype implementation of Fifth, a system that implements these techniques, and a preliminary empirical study of adaptive evaluation for a simple test program. In the test, the evaluation strategy adapts successfully to efficiently evaluate a query with pathological features that would prevent its evaluation by standard general-purpose strategies.

Logical Mistakes, Logical Aliens, and the Laws of Kant’s Pure General Logic

AbstractThere are two ways interpreters have tended to understand the nature of the laws of Kant’s pure general logic. On the first, these laws are unconditional norms for how we ought to think, and will govern anything that counts as thinking. On the second, these laws are formal criteria for being a thought, and violating them makes a putative thought not a thought. These traditions are in tension, in so far as the first depends on the possibility of thoughts that violate these laws, and the second makes violation impossible. In this essay I develop an interpretation of Kant’s pure general logic that overcomes this tension. It accounts for the possibility of logical mistakes, as the first tradition does, while still establishing the absolute impossibility of logical aliens, as the second tradition does. I then argue that the formalist insight that illogical exercises of the understanding are not alternative ways coherent thoughts could have been, but are mere confusions, is fundamental for achieving a proper understanding of the absolute normativity of the laws of pure general logic.

PURE LOGIC OF ITERATED FULL GROUND

AbstractThis article develops the Pure Logic of Iterated Full Ground (plifg), a logic of ground that can deal with claims of the form “ϕgrounds that (ψgroundsθ)”—what we call iterated grounding claims. The core idea is that some truths Γ ground a truthϕwhen there is an explanatory argument (of a certain sort) from premisses Γ to conclusionϕ. By developing a deductive system that distinguishes between explanatory and nonexplanatory arguments we can give introduction rules for operators for factive and nonfactive full ground, as well as for a propositional “identity” connective. Elimination rules are then found by using a proof-theoretic inversion principle.

Protecting Scientists from Gordon Gekko: How Organizations Use Hybrid Spaces to Engage with Multiple Institutional Logics

Previous work on institutional complexity has discussed two solutions that organizations internally deploy when externally engaging with multiple institutional logics: blended hybrids, in which logics are combined throughout the organization, and structural hybrids, in which different logics dominate in different compartments within the organization. While blended hybrids have been extensively investigated, few studies have examined how structural hybrids are constructed and maintained. We address this imbalance by studying university–industry research centers as instances of distinct organizational spaces used to engage with a minority logic. We found that these spaces require three kinds of work: (a) leveraging, where dominant logic practices are drawn on to achieve minority logic objectives; (b) hybridizing, where the practices inside the space are modified to allow engagement with the minority logic; and (c) bolstering, where the space is shielded against excessive minority logic influence and anchored back into the organization. Furthermore, contrary to the existing literature, we found that the spaces were hybrid, rather than being dominated by a single logic. Our finding is likely generalizable across many instances of structural hybrids given the integration problems that organizations with pure single logic spaces would face, combined with the usefulness of hybrid spaces. Our study is novel in revealing the work needed to sustain hybrid spaces and questioning the previously held conceptualization of structural hybrids as made up of single-logic compartments. The online appendix is available at https://doi.org/10.1287/orsc.2018.1228 .

The Transcendental Source of Logic by Way of Phenomenology

In this article I am going to argue for the possibility of a transcendental source of logic based on a phenomenologically motivated approach. My aim will be essentially carried out in two succeeding steps of reduction: the first one will be the indication of existence of an inherent temporal factor conditioning formal predicative discourse and the second one, based on a supplementary reduction of objective temporality, will be a recourse to a time-constituting origin which has to be assumed as a non-temporal, transcendental subjectivity and for that reason as possibly the ultimate transcendental root of pure logic. In the development of the argumentation and taking into account W.V. Quine’s views in his well-known Word and Object, a special emphasis will be given to the fundamentally temporal character of universal and existential predicative forms, to their status in logical theories in general, and to their underlying role in generating an inherently non-finitistic character reflected, for instance, in the undecidability of certain infinity statements in formal mathematical theories. This is shown also to concern metatheorems of such vital importance as Godel’s incompleteness theorems in mathematical foundations. Moreover in the course of the discussion the quest for the ultimate limits of predication will lead to the notions of separation and intentional correlation between an ‘observing’ subject and the object of ‘observation’ as well as to the notion of syntactical individuals taken as the irreducible non-analytic nuclei-forms within analytical discourse.