In
logic
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 o ...
, predicate abstraction is the result of creating a
predicate from a
formula
In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a ''chemical formula''. The informal use of the term ''formula'' in science refers to the general construct of a relationship betwe ...
. If Q is any formula then the predicate abstract formed from that sentence is (λx.Q), where λ is an
abstraction operator and in which every occurrence of x that is free in Q is bound by λ in (λx.Q). The resultant predicate (λx.Q(x)) is a monadic predicate capable of taking a
term t as argument as in (λx.Q(x))(t), which says that the object denoted by 't' has the property of being such that Q.
The states ( λx.Q(x) )(t) ≡ Q(t/x) where Q(t/x) is the result of replacing all free occurrences of x in Q by t. This law is shown to fail in general in at least two cases: (i) when t is irreferential and (ii) when Q contains
modal operator
A modal connective (or modal operator) is a logical connective for modal logic. It is an operator which forms propositions from propositions. In general, a modal operator has the "formal" property of being non- truth-functional in the following se ...
s.
In
modal logic
Modal logic is a kind of logic used to represent statements about Modality (natural language), necessity and possibility. In philosophy and related fields
it is used as a tool for understanding concepts such as knowledge, obligation, and causality ...
the "''
de re'' / ''de dicto'' distinction" is stated as
1. (DE DICTO):
2. (DE RE):
.
In (1) the modal operator applies to the formula A(t) and the term t is within the scope of the modal operator. In (2) t is ''not'' within the scope of the modal operator.
References
For the semantics and further philosophical developments of predicate abstraction see
Fitting and Mendelsohn, ''First-order Modal Logic'',
Springer
Springer or springers may refer to:
Publishers
* Springer Science+Business Media, aka Springer International Publishing, a worldwide publishing group founded in 1842 in Germany formerly known as Springer-Verlag.
** Springer Nature, a multinationa ...
, 1999.
Modal logic
Philosophical logic
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