A multiple-conclusion logic is one in which
logical consequence
Logical consequence (also entailment or logical implication) is a fundamental concept in logic which describes the relationship between statement (logic), statements that hold true when one statement logically ''follows from'' one or more stat ...
is a
relation
Relation or relations may refer to:
General uses
* International relations, the study of interconnection of politics, economics, and law on a global level
* Interpersonal relationship, association or acquaintance between two or more people
* ...
,
, between two
sets of
sentences
The ''Sentences'' (. ) is a compendium of Christian theology written by Peter Lombard around 1150. It was the most important religious textbook of the Middle Ages.
Background
The sentence genre emerged from works like Prosper of Aquitaine's ...
(or
proposition
A proposition is a statement that can be either true or false. It is a central concept in the philosophy of language, semantics, logic, and related fields. Propositions are the object s denoted by declarative sentences; for example, "The sky ...
s).
is typically interpreted as meaning that whenever each element of
is true, some element of
is true; and whenever each element of
is false, some element of
is false.
This form of logic was developed in the 1970s by
D. J. Shoesmith and
Timothy Smiley
Timothy John Smiley FBA (born 13 November 1930) is a British philosopher, appointed Emeritus Knightbridge Professor of Philosophy at Clare College, Cambridge University. He works primarily in philosophy of mathematics and logic.
Life and ca ...
[D. J. Shoesmith and T. J. Smiley, ''Multiple Conclusion Logic'', Cambridge University Press, 1978] but has not been widely adopted.
Some
logician
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arg ...
s favor a multiple-conclusion consequence relation over the more traditional single-conclusion relation on the grounds that the latter is
asymmetric (in the informal, non-mathematical sense) and favors truth over falsity (or assertion over denial).
See also
*
Sequent calculus
In mathematical logic, sequent calculus is a style of formal logical argumentation in which every line of a proof is a conditional tautology (called a sequent by Gerhard Gentzen) instead of an unconditional tautology. Each conditional tautolog ...
References
Logic
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