formation rule
Quick Summary
A formation rule in logic is a principle used to determine how to construct valid statements or formulas within a formalized language or calculus. These rules are fundamental to formal systems, ensuring that only grammatically correct and meaningful expressions can be formed.123
In the context of propositional calculus, formation rules define what constitutes a well-formed formula (wff). These rules typically start with basic elements, such as propositional variables (representing simple propositions), and then specify how these can be combined using logical operators (like "not," "and," "or," "if...then," and "if and only if") to create more complex propositions. For example, if 'p' and 'q' are wffs, then '~p' (not p) and '(p and q)' are also wffs, following specific structural guidelines.34
Formation rules are crucial for maintaining the consistency and completeness of logical systems, ensuring that all provable formulas are valid and that no contradictions arise.42
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formal logicThe lower predicate calculusThe formation rules are:
Read MoreThe formation rules are:
Read More- formal logicSpecial systems of LPC
…are added to LPC, the formation rules listed in the first paragraph of the section on the lower predicate calculus (see above The lower predicate calculus) need to be modified to enable the new symbols to be incorporated into wffs. This can be done as follows: A term is first…
Read More…are added to LPC, the formation rules listed in the first paragraph of the section on the lower predicate calculus (see above The lower predicate calculus) need to be modified to enable the new symbols to be incorporated into wffs. This can be done as follows: A term is first…
Read More - formal logicDefinite descriptions
As far as formation rules are concerned, definite descriptions can be incorporated into LPC by letting expressions of the form (ιa)α count as terms; rule 1′ above, in “Extensions of LPC,” will then allow them to occur in atomic formulas (including identity formulas). “The ϕ is (i.e., has…
Read MoreAs far as formation rules are concerned, definite descriptions can be incorporated into LPC by letting expressions of the form (ιa)α count as terms; rule 1′ above, in “Extensions of LPC,” will then allow them to occur in atomic formulas (including identity formulas). “The ϕ is (i.e., has…
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metalogicSyntax and semantics…usually requires a set of formation rules—i.e., a complete specification of the kinds of expressions that shall count as well-formed formulas (sentences or meaningful expressions), applicable mechanically, in the sense that a machine could check whether a candidate satisfies the requirements. This specification usually contains three parts: (1) a list…
Read More…usually requires a set of formation rules—i.e., a complete specification of the kinds of expressions that shall count as well-formed formulas (sentences or meaningful expressions), applicable mechanically, in the sense that a machine could check whether a candidate satisfies the requirements. This specification usually contains three parts: (1) a list…
Read More- metalogicFormation rules
The system may be set up by employing the following formation rules:
Read MoreThe system may be set up by employing the following formation rules:
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