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Faced with an unprovable statement, a complete proof procedure may sometimes succeed in detecting and signalling its unprovability. In the general case, where provability is only a
91:, which implies the existence of a complete but usually extremely inefficient proof procedure; however, a proof procedure is only of interest if it is reasonably efficient.
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or trees. A given proof procedure will target a specific proof calculus, but can often be reformulated so as to produce proofs in other proof styles.
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property, this is not possible, and instead the procedure will diverge (not terminate).
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There are several types of proof calculi. The most popular are
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if it produces a proof for each provable statement. The
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16:Systematic method for producing proofs
35:is a systematic method for producing
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87:of logical systems are typically
79:A proof procedure for a logic is
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47:Types of proof calculi used
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43:of (provable) statements.
108:Automated theorem proving
136:. Harvard Univ. Press.
89:recursively enumerable
23:, and in particular
69:semantic tableaux
53:natural deduction
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134:Methods of Logic
118:Deductive system
113:Proof complexity
63:-type systems),
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65:Hilbert systems
57:sequent calculi
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29:proof procedure
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41:proof calculus
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132:1982 (1950).
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130:Willard Quine
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96:semidecidable
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150:Proof theory
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75:Completeness
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31:for a given
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25:proof theory
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124:References
144:Category
102:See also
85:theorems
81:complete
39:in some
61:Gentzen
59:(i.e.,
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37:proofs
33:logic
21:logic
27:, a
19:In
146::
55:,
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