A multiple-conclusion logic is one in which
logical consequence
Logical consequence (also entailment) is a fundamental concept in logic, which describes the relationship between statements that hold true when one statement logically ''follows from'' one or more statements. A valid logical argument is on ...
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
*Public ...
,
, between two
sets of
sentences
''The Four Books of Sentences'' (''Libri Quattuor Sententiarum'') is a book of theology written by Peter Lombard in the 12th century. It is a systematic compilation of theology, written around 1150; it derives its name from the ''sententiae'' o ...
(or
proposition
In logic and linguistics, a proposition is the meaning of a declarative sentence. In philosophy, " meaning" is understood to be a non-linguistic entity which is shared by all sentences with the same meaning. Equivalently, a proposition is the no ...
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 car ...
[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 science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...
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 tautology i ...
References
Logic
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