Boolean Product of Zero-one Matrices Application to Truth Values of Logical Connectives of Several Propositions

2017 ◽  
Vol 21 (5) ◽  
pp. 1-5
Author(s):  
Etop Ndiyo
Keyword(s):  
Truth Values ◽  
Logical Connectives ◽  
Boolean Product

Fuzzy Logic and Mathematics

2017 ◽  
Author(s):  
Radim Belohlavek ◽  
Joseph W. Dauben ◽  
George J. Klir
Keyword(s):  
Fuzzy Logic ◽  
Common Ground ◽  
Fundamental Principle ◽  
Paradigm Shifts ◽  
Human Beings ◽  
Truth Values ◽  
Logical Connectives ◽  
Broad Variety ◽  
And Mathematics ◽  
Truth Degrees

The term “fuzzy logic” (FL) is a generic one, which stands for a broad variety of logical systems. Their common ground is the rejection of the most fundamental principle of classical logic—the principle of bivalence—according to which each declarative sentence has exactly two possible truth values—true and false. Each logical system subsumed under FL allows for additional, intermediary truth values, which are interpreted as degrees of truth. These systems are distinguished from one another by the set of truth degrees employed, its algebraic structure, truth functions chosen for logical connectives, and other properties. The book examines from the historical perspective two areas of research on fuzzy logic known as fuzzy logic in the narrow sense (FLN) and fuzzy logic in the broad sense (FLB), which have distinct research agendas. The agenda of FLN is the development of propositional, predicate, and other fuzzy logic calculi. The agenda of FLB is to emulate commonsense human reasoning in natural language and other unique capabilities of human beings. In addition to FL, the book also examines mathematics based on FL. One chapter in the book is devoted to overviewing successful applications of FL and the associated mathematics in various areas of human affairs. The principal aim of the book is to assess the significance of FL and especially its significance for mathematics. For this purpose, the notions of paradigms and paradigm shifts in science, mathematics, and other areas are introduced and employed as useful metaphors.

scholarly journals Truth Tables Without Truth Values: On 4.27 and 4.42 of Wittgenstein’s Tractatus

2021 ◽  
pp. 212-220
Author(s):  
Tabea Rohr
Keyword(s):  
Truth Values ◽  
Logical Connectives ◽  
Truth Tables ◽  
The Way

AbstractIn 4.27 and 4.42 of his Tractatus Wittgenstein introduces quite complicated formulas, which are equivalent to $$2^n$$ 2 n and $$2^{2^{n}}$$ 2 2 n . This paper shows, however, that the formulas Wittgenstein presents fit particularly well with the way he thinks about truth values, logical connectives, tautologies, and contradictions. Furthermore, it will be shown how Wittgenstein could have avoided truth values even more radically. In this way it is demonstrated that the reference to truth values can indeed be substituted by talking of existing and non-existing facts.

Development of the understanding of logical connectives.

1970 ◽  
Vol 61 (6, Pt.1) ◽  
pp. 451-460 ◽  
Author(s):  
Edith D. Neimark ◽  
Nan S. Slotnick
Keyword(s):  
Logical Connectives

Modal logics with Belnapian truth values

2010 ◽  
Vol 20 (3) ◽  
pp. 279-304 ◽  
Author(s):  
Serge P Odintsov ◽  
Heinrich Wansing
Keyword(s):  
Modal Logics ◽  
Truth Values

Truth-conditionality

2018 ◽  
Author(s):  
Juhani Yli-Vakkuri ◽  
John Hawthorne
Keyword(s):  
Thought Experiments ◽  
Truth Values ◽  
Narrow Content ◽  
Radical Form

In Chapter 2 we argue that internalists are committed to a kind of relativism, and that theirs is a particularly radical form of relativism. Thought experiments involving certain symmetries across space and/or time play a starring role. If the kinds of symmetries featured in them are possible, we argue, the truth values of narrow content must be relative to some very unusual parameters.

Logicism Reconsidered

2009 ◽  
Author(s):  
Agustín Rayo
Keyword(s):  
Fourth Section ◽  
Truth Values ◽  
The Third

This article is divided into four sections. The first two identify different logicist theses, and show that their truth-values can be established given minimal assumptions. The third section sets forth a notion of “content-recarving” as a possible constraint on logicist theses. The fourth section—which is largely independent from the rest of the article—is a discussion of “neologicism.”

scholarly journals Examining Automatic Stereotyping From a Propositional Perspective: Is Automatic Stereotyping Sensitive to Relational and Validity Information?

2021 ◽  
pp. 014616722110241
Author(s):  
Tal Moran ◽  
Jamie Cummins ◽  
Jan De Houwer
Keyword(s):  
Total N ◽  
Relational Information ◽  
Truth Values ◽  
Alternative Perspective ◽  
Automatic Stereotyping ◽  
Reference Person ◽  
Trait Associations

Research on automatic stereotyping is dominated by the idea that automatic stereotyping reflects the activation of (group–trait) associations. In two preregistered experiments (total N = 391), we tested predictions derived from an alternative perspective that suggests that automatic stereotyping is the result of the activation of propositional representations that, unlike associations, can encode relational information and have truth values. Experiment 1 found that automatic stereotyping is sensitive to the validity of information about pairs of traits and groups. Experiment 2 showed that automatic stereotyping is sensitive to the specific relations (e.g., whether a particular group is more or less friendly than a reference person) between pairs of traits and groups. Interestingly, both experiments found a weaker influence of validity/relational information on automatic stereotyping than on non-automatic stereotyping. We discuss the implications of these findings for research on automatic stereotyping.

scholarly journals The Liar Without Relativism

Erkenntnis ◽  
2021 ◽  
Author(s):  
Poppy Mankowitz
Keyword(s):  
Natural Language ◽  
Recent Literature ◽  
Liar Paradox ◽  
Full Understanding ◽  
Truth Values ◽  
The Liar ◽  
The Liar Paradox ◽  
Semantic Relativism

AbstractSome in the recent literature have claimed that a connection exists between the Liar paradox and semantic relativism: the view that the truth values of certain occurrences of sentences depend on the contexts at which they are assessed. Sagi (Erkenntnis 82(4):913–928, 2017) argues that contextualist accounts of the Liar paradox are committed to relativism, and Rudnicki and Łukowski (Synthese 1–20, 2019) propose a new account that they classify as relativist. I argue that a full understanding of how relativism is conceived within theories of natural language shows that neither of the purported connections can be maintained. There is no reason why a solution to the Liar paradox needs to accept relativism.

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