Concept
Guarded logic
Overview
Guarded logic is a choice set of dynamic logic involved in choices, where outcomes are limited.
A simple example of guarded logic is as follows: if X is true, then Y, else Z can be expressed in dynamic logic as (X?;Y)∪(~X?;Z). This shows a guarded logical choice: if X holds, then X?;Y is equal to Y, and ~X?;Z is blocked, and Y∪block is also equal to Y. Hence, when X is true, the primary performer of the action can only take the Y branch, and when false the Z branch.
A real-world example is the idea of paradox: something cannot be both true and false. A guarded logical choice is one where any change in true affects all decisions made down the line.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
Found by search and not yet checked by a person; they may only mention the idea in passing.
The prerogative instances are, as appears from what has preceded, twenty-seven in number, and are termed, solitary instances, migrating instances, conspicuous instances, clandestine instances, constitutive instances, similar instances, singular instances, deviating instances, bordering instances, instances of power, accompanying and hostile instances, subjunctive instances, instances of alliance, instances of the…
Francis Bacon, Novum organum
States what Guarded logic is.
[To say, that the rose is not red, implies that it is still coloured--in the first place with another colour; which however would be only one more positive judgment.] The individual however is not a universal. Hence (3) the judgment suffers disruption into one of two forms. It is either (a) the Identical judgment, an empty identical relation stating that the individual is the individual; or it is (b) what is called…
Georg Wilhelm Friedrich Hegel, The Logic of Hegel
States what Guarded logic is.
But it seems to us that they are misled by the ambiguity of the name. For argumentation signifies two things under one name, because any discussion respecting anything which is either probable or necessary is called argumentation, and so also is the systematic polishing of such a discussion. When then they bring forward any statement of this kind,--"Since she has had a child, she has lain, with a man," they bring…
Marcus Tullius Cicero, The Orations of Marcus Tullius Cicero, Volume 4
States what Guarded logic is.
Related ideas
- Automata theory
- First-order logic
- Mathematical logic
- Paradox
- Temporal logic
- Modal logic
- Second-order logic
- Dynamic logic (modal logic)
- Johan van Benthem (logician)
Place in the tradition
Part of Description logic.