scholarly journals The Dissolution of Bar-Hillel-Carnap Paradox by Semantic Information Theory Based on a Paraconsistent Logic

2018 ◽  
Vol 22 (1) ◽  
pp. 139-151
Author(s):  
Samir Gorsky
Keyword(s):  
Information Theory ◽  
Semantic Information ◽  
Paraconsistent Logic ◽  
Logical Structure ◽  
Theory Of Knowledge ◽  
Informational Content ◽  
Traditional Notion ◽  
Semantic Information Theory

Several logical puzzles, riddles and problems are defined based on the notion of games in informative contexts. Hintikka argues that epistemology or the theory of knowledge must be considered from the notion of information. So, knowledge cannot just be based on the notions of belief and justification. The present proposal will focus on the logical structure of information, and not only on the quantification of information as suggested by Claude A. Shannon (1916-2001) (Shannon 1948). In many cases, the information bits, although seemingly or factually contradictory, are quite relevant. The paraconsistent systems of logic offer a formalization of reasoning that can support certain contradictions. The well-known “Bar-Hillel–Carnap Paradox” (Bar-Hillel, 1964) causes embarrassment when it concludes that the informational content of a contradiction would be maximum, opposing the traditional notion that the semantic information must be true, and that contradictions are necessarily false.

scholarly journals THE SYSTEM OF PERSONAL PRONOUNS IN NATURAL LANGUAGE: A MEREOTOPOLOGICAL APPROACH

2021 ◽  
pp. 175-202
Author(s):  
Олег Анатольевич Доманов ◽  
Вадим Миронович Лурье ◽  
Ольга Владимировна Митренина
Keyword(s):  
Natural Language ◽  
Paraconsistent Logic ◽  
Logical Structure ◽  
Personal Pronouns ◽  
The Universe

Проанализирована логическая структура системы подлежащих естественного языка, выраженных местоимениями или аналогичными с лингвистической точки зрения, объектами, а именно: личными местоимениями, как эксплицитными, так и имплицитными, подлежащими неопределенно-личных и безличных (pro) предложений, а также нефинитных клауз (PRO). В процессе анализа оценивалось содержание имплицитных пропозиций, соответствующих тому или иному выбору подлежащего (агента) из универсума агентов. Для процедуры логического анализа был разработан мереотопологический метод, позволяющий работать как с классической, так и неконсистентными логиками. Показано, что подлежащие (агенты) в естественном языке могут выбираться как по процедурам, соответствующим классической логике, так и по процедурам, соответствующим различным неконсистентным логикам. А именно, подлежащие безличных предложений (pro) выбираются соответственно паракомплектной логике (допускающей контрарное противоречие), подлежащие нефинитных клауз (PRO) выбираются соответственно параконсистентной логике (допускающей субконтрарное противоречие), а подлежащие как неопределенно-личных, так и автореферентных предложений выбираются соответственно неалетической логике (допускающей контрадикторные противоречия). The logical structure of the system of subjects in the natural language is examined. The subjects were limited to those expressed by either pronouns or other similar (from a linguistic viewpoint) phenomena, namely: personal pronouns (both explicit and implicit), subjects of indefinite sentences, subjects of impersonal sentences (pro), and subjects of non-finite clauses (PRO). The implicit propositions corresponding to different modes of choosing the subjects (agents) from the universe of agents are analysed. For this purpose, a mereotopological method has been developed which allows to deal with both consistent (classical) and inconsistent logics. It was demonstrated that, in the natural language, the subjects (agents) can be chosen using the procedures that are governed by either consistent or inconsistent logic. Namely, the subjects of impersonal sentences (pro) are to be chosen according to the paracomplete logic (allowing the contrary contradiction), and the subjects of non-finite clauses (PRO), according to the paraconsistent logic (allowing the subcontrary contradiction), whereas the subjects of both indefinite and self-referential sentences are to be chosen according to the non-alethic logic (allowing the contradictory contradiction).

Seele und Paideia

1998 ◽  
pp. 61-69
Author(s):  
Michael Polemis
Keyword(s):  
Human Life ◽  
Theory Of Knowledge ◽  
Constituent Part ◽  
Traditional Notion ◽  
Modern Period ◽  
Philosophical Life ◽  
Kantian Theory ◽  
Meaningful Category ◽  
Scientific Value ◽  
Subjective Identity

Classical Greek philosophers, especially Plato and Aristotle, understood the soul as a necessary and constituent part of human life which manifests itself in the actualization of a dialectical relation between the philosophical life and virtue. Reflecting upon the Platonic and Aristotelian descriptions of soul along with the interpretation of this notion in Christianity, philosophers have continued to discuss soul in the modern period. The reliance on history has at the same time changed our understanding of soul, as in Hegelian idealism with its attempt to abrogate the traditional Kantian theory of knowledge which continued this trend towards an aporetic annulment of soul within the notion of history. Consequently, the traditional notion of paideia ceased to be a meaningful category for education, therefore, undermining the possibility of constructing an effective subjective identity for individuals as well as a theoretical access towards history. I will demonstrate how the traditional philosophical ideal that unified soul and paideia lost its appeal and scientific value, and will assess the ethical consequences of this pragmatic shift for future attempts to educate humanity. The analysis of this philosophical process will clearly indicate the conditions responsible for the demise of the notion of soul in philosophy, and will also consider the philosophers' options for a rehabilitation of soul in anticipation of the next century.

scholarly journals The P–T Probability Framework for Semantic Communication, Falsification, Confirmation, and Bayesian Reasoning

Philosophies ◽  
2020 ◽  
Vol 5 (4) ◽  
pp. 25
Author(s):  
Chenguang Lu
Keyword(s):  
Statistical Learning ◽  
Semantic Information ◽  
Likelihood Function ◽  
Probabilistic Logic ◽  
Bayesian Reasoning ◽  
Logical Probability ◽  
Statistical Probability ◽  
Truth Function ◽  
Semantic Communication ◽  
Semantic Information Theory

Many researchers want to unify probability and logic by defining logical probability or probabilistic logic reasonably. This paper tries to unify statistics and logic so that we can use both statistical probability and logical probability at the same time. For this purpose, this paper proposes the P–T probability framework, which is assembled with Shannon’s statistical probability framework for communication, Kolmogorov’s probability axioms for logical probability, and Zadeh’s membership functions used as truth functions. Two kinds of probabilities are connected by an extended Bayes’ theorem, with which we can convert a likelihood function and a truth function from one to another. Hence, we can train truth functions (in logic) by sampling distributions (in statistics). This probability framework was developed in the author’s long-term studies on semantic information, statistical learning, and color vision. This paper first proposes the P–T probability framework and explains different probabilities in it by its applications to semantic information theory. Then, this framework and the semantic information methods are applied to statistical learning, statistical mechanics, hypothesis evaluation (including falsification), confirmation, and Bayesian reasoning. Theoretical applications illustrate the reasonability and practicability of this framework. This framework is helpful for interpretable AI. To interpret neural networks, we need further study.

A Note on the Residual Entropy Function

1993 ◽  
Vol 7 (3) ◽  
pp. 413-420 ◽  
Author(s):  
Pietro Muliere ◽  
Giovanni Parmigiani ◽  
Nicholas G. Polson
Keyword(s):  
Information Theory ◽  
Probability Distribution ◽  
Random Variable ◽  
Reliability Theory ◽  
Entropy Function ◽  
Informational Content ◽  
Residual Entropy ◽  
Regularity Conditions ◽  
Information Theoretic ◽  
Information Theoretic Measures

Interest in the informational content of truncation motivates the study of the residual entropy function, that is, the entropy of a right truncated random variable as a function of the truncation point. In this note we show that, under mild regularity conditions, the residual entropy function characterizes the probability distribution. We also derive relationships among residual entropy, monotonicity of the failure rate, and stochastic dominance. Information theoretic measures of distances between distributions are also revisited from a similar perspective. In particular, we study the residual divergence between two positive random variables and investigate some of its monotonicity properties. The results are relevant to information theory, reliability theory, search problems, and experimental design.

scholarly journals Prefiguring Floridi’s Theory of Semantic Information

2013 ◽  
Vol 11 (2) ◽  
pp. 388-401
Author(s):  
John Mingers
Keyword(s):  
Information Theory ◽  
Embodied Cognition ◽  
Semantic Information ◽  
Philosophy Of Information ◽  
Ontological Status ◽  
The Social ◽  
Objective Interpretation ◽  
Luciano Floridi ◽  
Pragmatic Aspects ◽  
Forms Of Knowledge

Abstract: Luciano Floridi has been very active in helping to develop both the philosophy of information as a discipline and an actual theory of the nature of semantic information. This paper has three purposes. First, to demonstrate that Floridi’s information theory was largely prefigured by work carried out by Mingers and published some ten years earlier. This is simply a matter of setting the record straight, although the degree of commonality may provide some support for the theory. Second, to point out that there appears to be a degree of equivocation, or even contradiction, within Floridi’s theory concerning the ontological status of information – is it objective, independent of the receiver, or is it subjective, constructed by the receiver from the data they access? The paper argues strongly for an objective interpretation. Third, to point out extensions to Mingers’ theory in terms of the social and pragmatic aspects of language, the processing of information into meaning through embodied cognition, and the relation between information and different forms of knowledge  

scholarly journals Paraconsistent games and the limits of rational self-interest

2015 ◽  
Vol 12 (1) ◽  
Author(s):  
Arief Daynes ◽  
Panagiotis Andrikopoulos ◽  
Paraskevas Pagas ◽  
David Latimer
Keyword(s):  
Paraconsistent Logic ◽  
Logical Structure ◽  
Social Contexts ◽  
Order Logic ◽  
First Order Logic ◽  
Material Objects ◽  
Moral Choice ◽  
First Order ◽  
Moral Framework ◽  
Self Interest

It is shown that logical contradictions are derivable from natural translations into first order logic of the description and background assumptions of the Soros Game, and of other games and social contexts that exhibit conflict and reflexivity. The logical structure of these contexts is analysed using proof-theoretic and model-theoretic techniques of first order paraconsistent logic. It is shown that all the contradictions that arise contain the knowledge operator K. Thus, the contradictions do not refer purely to material objects, and do not imply the existence of inconsistent, concrete, physical objects, or the inconsistency of direct sensory experience. However, the decision-making of rational self-interested agents is stymied by the appearance of such intensional contradictions. Replacing the rational self-interest axioms with axioms for an appropriate moral framework removes the inconsistencies. Rational moral choice in conflict-reflexive social contexts then becomes possible.

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