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Augustus De Morgan’s Unpublished Octagon of Opposition
The British logician Augustus De Morgan (1806–1871) sought to unify the traditional syllogistics with the new algebraic logic that he and George...
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Pyomo.GDP: an ecosystem for logic based modeling and optimization development
We present three core principles for engineering-oriented integrated modeling and optimization tool sets—intuitive modeling contexts, systematic...
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Intelligent Decision-Support System for Epidemiological Diagnostics. II. Information Technologies Development*, **
The article projects the components of the intelligent decision support system for epidemiological diagnostics and investigates their interaction...
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On the complexity of the theory of a computably presented metric structure
We consider the complexity (in terms of the arithmetical hierarchy) of the various quantifier levels of the diagram of a computably presented metric...
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Extensions of the Positive Closure Operator by Using Logical Connectives
The positive closure operator is defined on using the logical formulas containing the logical connectives ∨, & and the quantifier ∃. Extensions of...
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RETRACTED ARTICLE: Lightweight multi-level authentication scheme for secured data transmission in IoT-Fog context
The IoT-sensed data is normally processed by Cloud Servers (CSs), but to reduce the cloud load and to avert network bandwidth wastage, Fog Computing...
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Peirce on Mathematical Reasoning and Discovery
Topics pertinent to mathematics concern the modes of reasoning in mathematics and their contribution to the discovery of new mathematical ideas,...
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Partitioning a Set of Vectors with Integer Coordinates by Means of Logical Hardware
The problem of partitioning a set of vectors with integer coordinates is considered with respect to the coordinate-wise and lexicographic order on...
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An Enriched Category Theory of Language: From Syntax to Semantics
State of the art language models return a natural language text continuation from any piece of input text. This ability to generate coherent text...
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Kant’s Antinomies of Pure Reason and the ‘Hexagon of Predicate Negation’
Based on an analysis of the category of “infinite judgments” in Kant, we will introduce the logical hexagon of predicate negation. This hexagon...
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Ingenuity
Euler’s demonstration of the impossibility of traversing the Könisgberg network without having to double back on one of its paths (previous chapter)...
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Disjunctive logic programs, answer sets, and the cut rule
In Minker and Rajasekar (J Log Program 9(1):45–74, 1990), Minker proposed a semantics for negation-free disjunctive logic programs that offers a...
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On Nonmonotonic Consequence Relations
We discuss nonmonotonic reasoning in terms of consequence relations and corresponding operators. Based on the matrix consequence that gives the...
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Reliability based maintenance programming by a new index for electrical distribution system components ranking
Reliability and accessibility of distribution systems are important goals that have significant impacts on the costs. The proper strategy of...
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Logic and Mathematics
The statistical theory of errors, which Peirce’s father applied in mathematics and astronomy, deeply influenced all principal concepts that cemented...
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A Categorical Framework for Modeling with Stock and Flow Diagrams
Stock and flow diagrams are already an important tool in epidemiology, but category theory lets us go further and treat these diagrams as...
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Color-Coded Epistemic Modes in a Jungian Hexagon of Opposition
This article considers distinct ways of understanding the world, referred in psychology as functions of consciousness or as cognitive modes, having...
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Logical Accidents and the Problem of the Inside Corner
With the emergence of computational design, the production of architecture has come to be dominated by the algorithm, yet the presence of algorithmic...
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Von Neumann Regular Hyperrings and Applications to Real Reduced Multirings
A multiring is a ring-like structure where the sum is multivalued and a hyperring is a multiring with a strong distributive property. With every...
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Lewis Carroll’s Almost Diagrammatic Logic Notation
There is growing literature on the employment of diagrams to ease logical reasoning. Less is said about the visual properties of symbolic notations....