Editing Temporal logic (section)

=== Syntax ===
The language of the logic first published in ''Podstawy Analizy Metodologicznej Kanonów Milla'' (''The Foundations of a Methodological Analysis of Mill’s Methods'') consisted of:<ref name=":0" />

* first-order logic operators ‘¬’, ‘∧’, ‘∨’, ‘→’, ‘≡’, ‘∀’ and ‘∃’
* realization operator U
* functional symbol δ
* propositional variables p<sub>1</sub>,p<sub>2</sub>,p<sub>3</sub>,...
* variables denoting time moments t<sub>1</sub>,t<sub>2</sub>,t<sub>3</sub>,...
* variables denoting time intervals n<sub>1</sub>,n<sub>2</sub>,n<sub>3</sub>,...

The set of terms (denoted by S) is constructed as follows:

* variables denoting time moments or intervals are terms
* if <math>\tau \in S</math> and <math>\epsilon</math> is a time interval variable, then <math>\delta(\tau, \epsilon) \in S</math>

The set of formulas (denoted by For) is constructed as follows:<ref name="Tkaczyk 2019 259–276"/>

* all first-order logic formulas are in <math>For</math>
* if <math>\tau \in S</math> and <math>\phi</math> is a propositional variable, then <math>U_{\tau}(\phi) \in For</math>
* if <math>\phi \in For</math>, then <math>\neg \phi \in For</math>
* if <math>\phi, \psi \in For</math> and <math>\circ \in \{\wedge, \vee, \rightarrow, \equiv\}</math>, then <math>\phi \circ \psi \in For</math>
* if <math>\phi \in For</math> and <math>Q \in \{\forall, \exists\}</math> and υ is a propositional, moment or interval variable, then <math>Q_{\upsilon}\phi \in For</math>