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In term logic (a branch of philosophical logic), the square of opposition is a diagram representing the relations between the four basic categorical propositions. The origin of the square can be traced back to Aristotle 's tractate On Interpretation and its distinction between two oppositions: contradiction and contrariety .
Description: Square of opposition. In the Venn diagrams black areas tell, that the area is empty and red areas tell, that there is at least one element.. Faded red areas and faded arrows apply only in classical logic, where only nonempty domains are used.
The logical hexagon extends the square of opposition to six statements. In philosophical logic, the logical hexagon (also called the hexagon of opposition) is a conceptual model of the relationships between the truth values of six statements. It is an extension of Aristotle's square of opposition.
Square of opposition In the Venn diagrams black areas are empty and red areas are nonempty. The faded arrows and faded red areas apply in traditional logic. Boolean logic is a system of syllogistic logic invented by 19th-century British mathematician George Boole, which attempts to incorporate the "empty set", that is, a class of non-existent entities, such as round squares, without resorting ...
This diagram shows the contradictory relationships between categorical propositions in the square of opposition of Aristotelian logic. In traditional logic, a contradiction occurs when a proposition conflicts either with itself or established fact. It is often used as a tool to detect disingenuous beliefs and bias.
In model theory, a branch of mathematical logic, the diagram of a structure is a simple but powerful concept for proving useful properties of a theory, ...
A syllogism (Ancient Greek: συλλογισμός, syllogismos, 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true.
In artificial intelligence, a sentential decision diagram (SDD) is a type of knowledge representation used in knowledge compilation to represent Boolean functions. SDDs can be viewed as a generalization of the influential ordered binary decision diagram (OBDD) representation, by allowing decisions on multiple variables at once.