Truth-functional Research Articles

Stability Analysis of Diabetes Mellitus Model in Neutrosophic Fuzzy Environment

Neutrosophic differential equation (NDE) plays a vital role in mathematical modeling on uncertainty during last few years.It is established that NDE comprises a neutrosophic number whose membership function contains three parts like as truth function, indeterministic and falsity functions.In this paper, a diabetes mellitus model has been formulated in neutrosophic fuzzy environment to get more realistic mathematical model. The initial conditions of diabetes system are considered as trapezoidal neutrosophic fuzzy number. The concept of NDE via nuetrosophic generalised derivative of type-1 and type-2 has used in this article. This is the first article in which the stability analysis of diabetes model in neutrosophic environment is introduced. The existence of strong solution and weak neutrosophic solution of the proposed system are employed in the manuscript. Also, we have exposed the comparison of the suggested model between fuzzy environment and neutrosophic environment.The all results, formulas are confirmed graphically and numerically by MATLAB software.

Kierkegaard’s Theories of the Stages of Existence and Subjective Truth as a Model for Further Research into the Phenomenology of Religious Attitudes

There are many religions in the human world, and people manifest their religiousness in many different ways. The main problem this paper addresses concerns the possibility of sorting out this complex world of human religiousness by showing that it can be phenomenologically reduced to a few very basic existential attitudes. These attitudes express the main types of ways in which a human being relates to his or herself and the world, independently of the worldview or religion professed by the individual. I use Kierkegaard’s theories of the stages of existence and subjective truth as a model. The theory of the stages of existence provides five basic existential attitudes on the basis of which religious attitudes can develop: spiritlessness, the aesthetic, the ethical, religiousness A, and religiousness B. The theory of subjective truth shows how the concept of truth functions in an ethical and existential sense as the personal truth of an individual engaged in building their religious identity. In turn, I discuss the problem of the relation of Kierkegaard’s philosophy to phenomenology, briefly introduce his concept of subjective truth and the stages of existence, and show how existential attitudes can be transformed into religious ones. I also consider the problem of the demonic as the inverted order of this anthropological and existential model. Finally, I argue that the model developed herein may be useful for further research into the phenomenology of religious attitudes.

Attribute implications in multi-adjoint concept lattices with hedges

The computation of (if-then) rules relating the most representative variables of a given dataset is a relevant goal in different areas of data analysis such as stock market prediction, disease diagnosis and census data analysis, among others. In Formal Concept Analysis (FCA), attribute implications follow the philosophy of the if-then rules establishing relationships between sets of attributes. This paper will focus on the theoretical development of attribute implications through the tools provided by the multi-adjoint concept lattice framework. We will show different notions to compute the validity of attribute implications, analyzing their properties and comparing the proposed alternatives. The use of linguistic hedges, and truth-stressing hedges in particular, is an interesting way of incorporating truth functions into attribute implications. Moreover, they have been considered in the computation of the concepts of a given context. This paper also introduces and studies the main properties of the multi-adjoint concept lattices framework with truth-stressing hedges.

AN ALGEBRAIC PROOF OF COMPLETENESS FOR MONADIC FUZZY PREDICATE LOGIC

Abstract Monoidal t-norm based logic $\mathbf {MTL}$ is the weakest t-norm based residuated fuzzy logic, which is a $[0,1]$ -valued propositional logical system having a t-norm and its residuum as truth function for conjunction and implication. Monadic fuzzy predicate logic $\mathbf {mMTL\forall }$ that consists of the formulas with unary predicates and just one object variable, is the monadic fragment of fuzzy predicate logic $\mathbf {MTL\forall }$ , which is indeed the predicate version of monoidal t-norm based logic $\mathbf {MTL}$ . The main aim of this paper is to give an algebraic proof of the completeness theorem for monadic fuzzy predicate logic $\mathbf {mMTL\forall }$ and some of its axiomatic extensions. Firstly, we survey the axiomatic system of monadic algebras for t-norm based residuated fuzzy logic and amend some of them, thus showing that the relationships for these monadic algebras completely inherit those for corresponding algebras. Subsequently, using the equivalence between monadic fuzzy predicate logic $\mathbf {mMTL\forall }$ and S5-like fuzzy modal logic $\mathbf {S5(MTL)}$ , we prove that the variety of monadic MTL-algebras is actually the equivalent algebraic semantics of the logic $\mathbf {mMTL\forall }$ , giving an algebraic proof of the completeness theorem for this logic via functional monadic MTL-algebras. Finally, we further obtain the completeness theorem of some axiomatic extensions for the logic $\mathbf {mMTL\forall }$ , and thus give a major application, namely, proving the strong completeness theorem for monadic fuzzy predicate logic based on involutive monoidal t-norm logic $\mathbf {mIMTL\forall }$ via functional representation of finitely subdirectly irreducible monadic IMTL-algebras.

How ambiguity codes specify molecular descriptors and information flow in Code Biology

The article presents IUPAC ambiguity codes for incomplete nucleic acid specification, and their use in Code Biology. It is shown how to use this nomenclature in order to extract accurate information on different properties of the biological systems. We investigated the use of ambiguity codes, as mathematical and logical operators and truth table elements, for the encoding of amino acids by means of the Standard Genetic Code. It is explained how to use ambiguity codes and truth functions in order to obtain accurate information on different properties of the biological systems. Nucleotide ambiguity codes could be applied to: 1. encoding descriptive information of nucleotides, amino acids and proteins (e.g., of polarity, relative solvent accessibility, atom depth, etc.), and 2. system modelling ranging from standard bioinformatics tools to classic evolutionary models (i.e. from Miyazawa−Jernigan statistical potential to Kimura three-substitution-type model, respectively). It is shown that the algorithms based on IUPAC ambiguity codes, Boolean functions and truth table, Probabilistic Square of Opposition/Semiotic Square and Klein 4-groups—could be used for the bioinformatics analyses and Relational data modelling in natural science. Underlying mathematical, logical and semiotic concepts of interest are presented and addressed.

Live blogs can’t handle the truth? A contemporary cross-cultural consideration of transparency and procedural justice

Reporting from trials using live blogs to continuously inform readers about courtroom events have rapidly become an established part of legal life and are often assumed to fulfill demands of open justice. However, a deep sociolegal understanding of how legal professionals perceive live blogs as affecting procedural justice is currently missing, as is a thick understanding of what transparency means to legal professionals. As more detailed knowledge on contemporary transparency will contribute to understanding the acceptance and resistance to open justice and specific reporting formats, this study focuses on the interlinking of legal professionals, transparency and live blogs. A qualitative cross-cultural approach finds that legal professionals consider Bentham’s tenets to be partially transformed, in particular regarding the original truth function. Rather than enabling truths, legal professionals perceive live blogs as a threat to truths. Nevertheless, live blogs are considered to provide good enough transparency in relation to specific jurisdictional contexts.

Tractatus 6 Reconsidered: An Algorithmic Alternative to Wittgenstein's Trade-Off

Wittgenstein's conception of the general form of a truth function given in thesis 6 can be presented as a sort of a trade-off: the author of the Tractatus is unable to reconcile the simplicity of his original idea of a series of forms with the simplicity of his generalisation of Sheffer's stroke; therefore, he is forced to sacrifice one of them. As we argue in this paper, the choice he makes – to weaken the logical constraints put on the concept of a series of forms, thus effectively metaphorising that concept for the sake of upholding the N-operation's role of generating the series – is unfortunate. An actual expansion of a series of truth functions as defined in 6 would require either making decisions at each step (Anscombe) or outwardly rejecting the concept of a series (Sundholm). However, neither is faithful to Wittgenstein's own fundamental intuitions regarding the nature of logic. For this reason, a different trade-off that prioritises upholding the basic features of a series of forms over the simplicity of the operation that generates that series seems to be much more reasonable. We offer such a trade-off by developing the schema already present in the Tractatus (5.101). The key element of our alternative solution is the construction of an operation that can perform the task of producing all consecutive truth functions of a given collection of atomic propositions as an invariant difference between any base and its successor throughout the series. We define it as a composition of three functions (in an algebraic sense): the first turns a symbol of a given truth function into a binary number, the second increments that number, the third turns the result back into a symbol of another truth function. We also show how the operation can be defined by means of a different notation without invoking binary arithmetic.

Truth‐value relations and logical relations

AbstractAfter some generalities about connections between functions and relations in Sections 1 and 2 recalls the possibility of taking the semantic values of ‐ary Boolean connectives as ‐ary relations among truth‐values rather than as ‐ary truth functions. Section 3, the bulk of the paper, looks at correlates of these truth‐value relations as applied to formulas, and explores in a preliminary way how their properties are related to the properties of “logical relations” among formulas such as equivalence, implication (entailment) and contrariety (logical incompatibility), concentrating for illustrative purposes on binary logical relations such as those just listed. To avoid an excess of footnotes, some points have been deferred to an Appendix as “Longer Notes”.

О локальной согласованности нечетких означиваний

The paper is devoted to the model-theoretic formalization of the semantic model of the object domain. The article discusses the concept of a fuzzy model, which is a model where the truth function exhibits properties of a fuzzy measure. We demonstrate that a fuzzy model is a generalization of the concept of fuzzification of a precedent (semantic) model to include a countable number of precedents. In practice, it is common to have partial expert knowledge about the set of events in the object domain, making it difficult to immediately describe the fuzzy model. Additionally, since expert valuations are subjective, they may be incorrect and inconsistent with any fuzzy model. In the article, we introduce the concepts of coordinated and locally coordinated valuation of a set of sentences, and provide proofs for interval theorems and an analogue of the compactness theorem.

Schleier (Veil)

The motif of the Schleier (veil) can be found throughout Goethe’s works, where it is often associated with images of textual production. In so doing, Goethe builds on a rich literary tradition of comparing the production of verbal works of art with the making of fabrics and the art of weaving. The following entry isolates and analyzes some representative instances of this lexeme in which the veil is used to evoke not only the traditional semantic field of textiles and their crafts as models for verbal works of art but also this lexeme’s potential in regard to epistemological and perceptual concerns. It will thereby trace the veil’s emergence as a “thing to think with” when it concerns the truth function of poetry and show how, as a conceptual metaphor, it invites reflection on the verbal work of art as an exceptional means of negotiating the position between perception and truth, the sacred and the profane, the eternal and the ephemeral, and the local and the global. In modelling this mediation in Goethe’s oeuvre, the veil lies at the intersection of poetology and epistemology. It also offers a reflection on the human subject’s position vis-à-vis the world and on the work of art’s position with regard to temporality and ever-changing historical contexts.

The Imaginary Force of History: On Images, the Imaginary, and Myths in Foucault’s Early Works

ABSTRACT In manuscripts and unpublished articles written in the 1950s, Foucault developed a notion of myth that was intimately linked to what he called “imaginary forces,” a notion that he framed as a new critical approach. Its most important functions lie in exposing how mythological narratives naturalize social processes, and in developing a skeptical stance towards the allegedly liberating function of truth. This notion of myth is central in History of Madness, but it features most prominently in a passage that was omitted from the first English translation. Here, Foucault criticizes the narrative that Enlightenment psychiatry told about its own origins, which naturalized social processes. The young Foucault’s notion of myth is strikingly similar to the Marxist notion of second nature.

Effect of the Choice of Connectives on the Relation between Classical Logic and Intuitionistic Logic

In this paper, we study general propositional connectives characterized by truth functions and provide a necessary and sufficient condition for intuitionistic logic that coincides with classical logic.

The Function of Truth and the Conservativeness Argument

Abstract Truth is often considered to be a logico-linguistic tool for expressing indirect endorsements and infinite conjunctions. In this article, I will point out another logico-linguistic function of truth: to enable and validate what I call a blind argument, namely, an argument that involves indirectly endorsed statements. Admitting this function among the logico-linguistic functions of truth has some interesting consequences. In particular, it yields a new type of so-called conservativeness argument, which poses a new type of threat to deflationism about truth.

Using the Semantic Information G Measure to Explain and Extend Rate-Distortion Functions and Maximum Entropy Distributions.

In the rate-distortion function and the Maximum Entropy (ME) method, Minimum Mutual Information (MMI) distributions and ME distributions are expressed by Bayes-like formulas, including Negative Exponential Functions (NEFs) and partition functions. Why do these non-probability functions exist in Bayes-like formulas? On the other hand, the rate-distortion function has three disadvantages: (1) the distortion function is subjectively defined; (2) the definition of the distortion function between instances and labels is often difficult; (3) it cannot be used for data compression according to the labels’ semantic meanings. The author has proposed using the semantic information G measure with both statistical probability and logical probability before. We can now explain NEFs as truth functions, partition functions as logical probabilities, Bayes-like formulas as semantic Bayes’ formulas, MMI as Semantic Mutual Information (SMI), and ME as extreme ME minus SMI. In overcoming the above disadvantages, this paper sets up the relationship between truth functions and distortion functions, obtains truth functions from samples by machine learning, and constructs constraint conditions with truth functions to extend rate-distortion functions. Two examples are used to help readers understand the MMI iteration and to support the theoretical results. Using truth functions and the semantic information G measure, we can combine machine learning and data compression, including semantic compression. We need further studies to explore general data compression and recovery, according to the semantic meaning.

Sample logic

Abstract The need for a ‘many-valued logic’ in linguistics has been evident since the 1970s, but there was lack of clarity as to whether it should come from the family of fuzzy logics or from the family of probabilistic logics. In this regard, Fine [14] and Kamp [26] pointed out undesirable effects of fuzzy logic (the failure of idempotency and coherence) which kept two generations of linguists and philosophers at arm’s length. (Another unwanted feature of fuzzy logic is the property of truth functionality.) While probabilistic logic is not fraught by the same problems, its lack of constructiveness, i.e. its inability to compose complex truth degrees from atomic truth degrees, did not make it more attractive to linguists either. In the absence of a clear perspective in ‘many-valued logic’, scholars chose to proliferate ontologies grafted atop the classical bivalent logic: ontologies for truth, individuals, events, situations, possible worlds and degrees. The result has been a collection of incompatible classical logics. In this paper, I present sample logic, in particular its semantics (not its axiomatization). Sample logics is a member of the family of probabilistic logics, which is constructive without being truth functional. More specifically, I integrate all the important linguistic data on which the classical logics are predicated. The concepts of (in)dependency and conditional (in)dependency are the cornerstones of sample logic.

Consistency Fuzzy Sets and a Cosine Similarity Measure in Fuzzy Multiset Setting and Application to Medical Diagnosis

The main purpose of this study is to construct a base for a new fuzzy set concept that is called consistency fuzzy set (CFS) which expresses the multidimensional uncertain data quite successfully. Our motive is to reduce the complexity and difficulty caused by the information contained in the truth sequence in a fuzzy multiset (FMS) and to present the data of the truth sequence in a more understandable and compact manner. Therefore, this paper introduces the concept of CFS that is characterized with a truth function defined on a universal set 0,1 2 . The first component of the truth pair of a CFS is the average value of the truth sequence of a FMS and the second component is the consistency degree, that is, the fuzzy complement of the standard deviation of the truth sequence of the same FMS. The main contribution of a CFS is the reflection of both the level of the average of the data that can be expressed with the different sequence lengths and the degree of the reasonable information in data via consistency degree. To develop this new concept, this paper also presents a correlation coefficient and a cosine similarity measure between CFSs. Furthermore, the proposed correlation coefficient and cosine similarity measure are applied to a multiperiod medical diagnosis problem. Finally, a comparison analysis is given between the obtained results and the existing results in literature to show the efficiency and rationality of the proposed correlation coefficient and cosine similarity measure.

A Framework of Learning Through Empirical Gain Maximization.

We develop in this letter a framework of empirical gain maximization (EGM) to address the robust regression problem where heavy-tailed noise or outliers may be present in the response variable. The idea of EGM is to approximate the density function of the noise distribution instead of approximating the truth function directly as usual. Unlike the classical maximum likelihood estimation that encourages equal importance of all observations and could be problematic in the presence of abnormal observations, EGM schemes can be interpreted from a minimum distance estimation viewpoint and allow the ignorance of those observations. Furthermore, we show that several well-known robust nonconvex regression paradigms, such as Tukey regression and truncated least square regression, can be reformulated into this new framework. We then develop a learning theory for EGM by means of which a unified analysis can be conducted for these well-established but not fully understood regression approaches. This new framework leads to a novel interpretation of existing bounded nonconvex loss functions. Within this new framework, the two seemingly irrelevant terminologies, the well-known Tukey's biweight loss for robust regression and the triweight kernel for nonparametric smoothing, are closely related. More precisely, we show that Tukey's biweight loss can be derived from the triweight kernel. Other frequently employed bounded nonconvex loss functions in machine learning, such as the truncated square loss, the Geman-McClure loss, and the exponential squared loss, can also be reformulated from certain smoothing kernels in statistics. In addition, the new framework enables us to devise new bounded nonconvex loss functions for robust learning.

Semidisquotation and the infinitary function of truth

The infinitary function of the truth predicate consists in its ability to express infinite conjunctions and disjunctions. A transparency principle for truth states the equivalence between a sentence and its truth predication; it requires an introduction principle—which allows the inference from “snow is white” to “the sentence ‘snow is white’ is true”—and an elimination principle—which allows the inference from “the sentence ‘snow is white’ is true” to “snow is white”. It is commonly assumed that a theory of truth needs to satisfy a transparency principle to fulfil the infinitary function. Picollo and Schindler (Erkenntnis 83:899–928, 2017) argue against this idea. They prove that, given certain assumptions, an elimination principle is sufficient for the purpose. Then, they pose a challenge: to show why we should incorporate introduction principles to our theory of truth. In this essay I take on the challenge. I show that, given the authors’ assumptions, an introduction principle is also sufficient to perform the infinitary function.

Why Did F. P. Ramsey Never Repeat the Claims He Had Made on the First Page of His Jan., 1922 Cambridge Magazine Three Page Note Concerning Keynes’s Logical Theory of Probability?: It Is Easy for a Reader To See That Ramsey’s Review Is Dead Wrong if That Reader Has Actually Read the 'A Treatise on Probability'

The first page of the 18 year old, F. P. Ramsey’s very short three page review, in the Cambridge Magazine issue of Jan., 1922, of Keynes’s A Treatise on Probability is comprised of claims about Keynes’s logical theory of probability that, to use L. J. Savage’s characterization of academics who tried to apply his Subjective Expected Utility model to Large Worlds (macro, intertemporal, long run decision making), as opposed to Small Worlds (micro ,short run decision making), was “utterly preposterous” and complete ”nonsense”. Ramsey’s very small review was obviously never refereed J. M. Keynes and/or Bertrand Russell could have made short work of the 18 year old Ramsey’s note in a few minutes, thereby permanently ending his academic career at Cambridge before it ever had a chance to get started. However, they decided not to do so, as they recognized that Ramsey had special intellectual gifts, although they were clearly undeveloped at the time. Keynes decided to take Ramsey under his wing and train him. The very, very severe problems with the first page consist of two claims made by Ramsey. The first claim made by F. P. Ramsey is that: “We have, then, numerous probability relations; these it is commonly supposed are all numerical, that is, correlated with the real numbers from 0 to 1 in such a way that the ordinary rules of the probability calculus hold, e.g., that the product of the numbers correlated with two probabilities is equal to the number correlated with the product (in Mr. Keynes' sense) of the two probabilities. Mr. Keynes denies this; he supposes not only that not all probabilities are numerical, but also that it is possible to have two probabilities which are unequal and such that neither is greater than the other. This view is based on the difficulty in so many cases of saying with any confidence which of two probabilities is the greater, or of assigning any numerical measures to them. But it would appear that the force of this objection to the ordinary view is exaggerated to Mr. Keynes for two reasons.” The second claim made by F.P. Ramsey is that: “First, he thinks that between any two non-self-contradictory propositions there holds a probability relation (Axiom I), for example between 'My carpet is blue' and 'Napoleon was a great general'; it is easily seen that it leads to contradictions to assign the probability 1/2 to such cases, and Mr. Keynes would conclude that the probability is not numerical. But it would seem that in such cases there is no probability; that, for a logical relation, other than a truth function, to hold between two propositions, there must be some connection between them. If this be so, there is no such probability as the probability that 'my carpet is blue' given only that 'Napoleon was a great general', and there is therefore no question of assigning a numerical value.” Ramsey’s first claim is the result of his gross ignorance of Keynes’s imprecise, interval valued ,non additive approach to probability, as was illustrated by Keynes in the discussions of the beauty contest problem on pp.25-28, as well as by six other illustrations contained in Chapter III of the A Treatise on Probability. The mathematical analysis was presented in Part II of the book, a part that Ramsey never got around to ever reading in his lifetime. The second claim made by Ramsey has nothing to do with Keynes’s use of propositions, which must be stated in the form of an argument- one proposition must contain relevant evidence while the second proposition must be a conclusion with respect to the proposition containing the relevant evidence. Only then is a relation of logical probability present. Nowhere at any place in his A Treatise on Probability or any other work written in Keynes’s lifetime did Keynes state: “…that between any two non-self-contradictory propositions there holds a probability relation (Axiom I)…” There is no such Axiom I in Keynes’s A Treatise on Probability. Therefore, Ramsey’s”… 'My carpet is blue' and 'Napoleon was a great general…” example is an oxymoron because his two propositions do not form an argument. The current belief among academics, that has been a belief for 100 years, that Ramsey not only destroyed and demolished Keynes’s logical theory of probability, but that Keynes himself felt compelled by the overwhelming logical power of Ramsey’s critique to accept Ramsey’s critique and adopted a subjective theory of probability himself, calls into question the claims made by academics writing on Keynes that they are publishing scientific works that contribute to the growth of knowledge. All I see is utter and complete nonsense.

I principi della sintassi semantica

Semantic Syntax (SeSyn), originally called Generative Semantics, is an offshoot of Chomskyan generative grammar (ChoGG), rejected by Chomsky and his school in the late 1960s. SeSyn is the theory of algorithmical grammars producing the well-formed sentences of a language L from the corresponding semantic input, the Semantic Analysis (SA), represented as a traditional tree structure diagram in a specific formal language of incremental predicate logic with quantifying and qualifying operators (including the truth functions), and with all lexical items filled in. A SeSyn-type grammar is thus by definition transformational, but not generative. The SA originates in cognition in a manner that is still largely mysterious, but its actual form can be distilled from the Surface Structure (SS) of the sentences of L following the principles set out in SeSyn. In this presentation we provide a more or less technical résumé of the SeSyn theory. A comparison is made with ChoGG-type grammars, which are rejected on account of their intrinsic unsuitability as a cognitive-realist grammar model. The ChoGG model follows the pattern of a 1930s neopositivist Carnap-type grammar for formal logical languages. Such grammars are random sentence generators, whereas, obviously, (nonpathological) humans are not. A ChoGG-type grammar is fundamentally irreconcilable with a mentalist-realist theory of grammar. The body of the paper consists in a demonstration of the production of an English and a French sentence, the latter containing a classic instance of the cyclic rule of Predicate Raising (PR), essential in the general theory of clausal complementation yet steadfastly repudiated in ChoGG for reasons that have never been clarified. The processes and categories defined in SeSyn are effortlessly recognised in languages all over the world, whether indigenous or languages of a dominant culture—taking into account language-specific values for the general theoretical parameters involved. This property makes SeSyn particularly relevant for linguistic typology, which now ranks as the most promising branch of linguistics but has so far conspicuously lacked an adequate theoretical basis.