A multiple-conclusion logic is one in which logical consequence is a relation,

\vdash

, 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'' ...

(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).

\Gamma \vdash \Delta

is typically interpreted as meaning that whenever each element of

\Gamma

is true, some element of

\Delta

is true; and whenever each element of

\Delta

is false, some element of

\Gamma

is false. This form of logic was developed in the 1970s by

D. J. Shoesmith D. or d. may refer to, usually as an abbreviation: * Don (honorific), a form of address in Spain, Portugal, Italy, and their former overseas empires, usually given to nobles or other individuals of high social rank. * Date of death, as an abbreviati ...

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 Mathematical logic, formal and informal logic. Formal logic is the science of Validity (logic), deductively valid inferences or of logical truths. It is a formal science investigating h ...

s favor a multiple-conclusion consequence relation over the more traditional single-conclusion relation on the grounds that the latter is

asymmetric Asymmetric may refer to: *Asymmetry in geometry, chemistry, and physics Computing * Asymmetric cryptography, in public-key cryptography *Asymmetric digital subscriber line, Internet connectivity * Asymmetric multiprocessing, in computer architect ...

(in the informal, non-mathematical sense) and favors truth over falsity (or assertion over denial).

References

Logic {{logic-stub

See also

References