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Что (кто) такое propositional logic - определение
BRANCH OF LOGIC CONCERNED WITH THE STUDY OF PROPOSITIONS (WHETHER THEY ARE TRUE OR FALSE) THAT ARE FORMED BY OTHER PROPOSITIONS WITH THE USE OF LOGICAL CONNECTIVES, AND HOW THEIR VALUE DEPENDS ON THE TRUTH VALUE OF THEIR COMPONENTS
Sentential logic; Sentential calculus; Propositional logic; Sentence logic; Sentance logic; Propositional Calculus; Truth-functional propositional logic; Propositional calculi; Truth-functional propositional calculus; Classical propositional logic; Exportation in logic; Solvers for propositional logic formulas; History of propositional calculus; Truth functional propositional calculus; Truth functional propositional logic
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propositional logic
<logic> (or "propositional calculus") A system of {symbolic
logic} using symbols to stand for whole propositions and
logical connectives. Propositional logic only considers
whether a proposition is true or false. In contrast to
predicate logic, it does not consider the internal structure
of propositions.
(2002-05-21)
propositional calculus
Propositional calculus
Propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic.
Timed propositional temporal logic
TPTL; Timed Propositional Temporal Logic
In model checking, a field of computer science, Timed Propositional Temporal Logic (TPTL) is an extension of Linear Temporal Logic (LTL) in which variables are introduced to measure times between two events. For example, while LTL allows to state that each event p is eventually followed by an event q, TPTL furthermore allows to give a time limit for q to occur.
intuitionist logic
![The [[Rieger–Nishimura lattice]]. Its nodes are the propositional formulas in one variable up to intuitionistic [[logical equivalence]], ordered by intuitionistic logical implication.](https://commons.wikimedia.org/wiki/Special:FilePath/Rieger-Nishimura.svg?width=200 "The [[Rieger–Nishimura lattice]]. Its nodes are the propositional formulas in one variable up to intuitionistic [[logical equivalence]], ordered by intuitionistic logical implication.")
VARIOUS SYSTEMS OF SYMBOLIC LOGIC
Constructivist logic; Constructive logic; Intuitionist logic; Intuitionistic propositional calculus; Intuitionistic Prop Calc; Intuitionistic Logic; Semantics of intuitionistic logic; Semantics for intuitionistic logic
<spelling> Incorrect term for "intuitionistic logic".
(1999-11-24)
intuitionistic logic
VARIOUS SYSTEMS OF SYMBOLIC LOGIC
Constructivist logic; Constructive logic; Intuitionist logic; Intuitionistic propositional calculus; Intuitionistic Prop Calc; Intuitionistic Logic; Semantics of intuitionistic logic; Semantics for intuitionistic logic
<logic, mathematics> Brouwer's foundational theory of
mathematics which says that you should not count a proof of
(There exists x such that P(x)) valid unless the proof
actually gives a method of constructing such an x. Similarly,
a proof of (A or B) is valid only if it actually exhibits
either a proof of A or a proof of B.
In intuitionism, you cannot in general assert the statement (A
or not-A) (the principle of the excluded middle); (A or
not-A) is not proven unless you have a proof of A or a proof
of not-A. If A happens to be undecidable in your system
(some things certainly will be), then there will be no proof
of (A or not-A).
This is pretty annoying; some kinds of perfectly
healthy-looking examples of proof by contradiction just stop
working. Of course, excluded middle is a theorem of
classical logic (i.e. non-intuitionistic logic).
{History
(http://britanica.com/bcom/eb/article/3/0,5716,118173+14+109826,00.html) }.
(2001-03-18)
Intuitionistic logic
VARIOUS SYSTEMS OF SYMBOLIC LOGIC
Constructivist logic; Constructive logic; Intuitionist logic; Intuitionistic propositional calculus; Intuitionistic Prop Calc; Intuitionistic Logic; Semantics of intuitionistic logic; Semantics for intuitionistic logic
Intuitionistic logic, sometimes more generally called constructive logic, refers to systems of symbolic logic that differ from the systems used for classical logic by more closely mirroring the notion of constructive proof. In particular, systems of intuitionistic logic do not include the law of the excluded middle and double negation elimination, which are fundamental inference rules in classical logic.
Second-order propositional logic
TYPE OF PROPOSITIONAL LOGIC
Second-order Boolean
A second-order propositional logic is a propositional logic extended with quantification over propositions. A special case are the logics that allow second-order Boolean propositions, where quantifiers may range either just over the Boolean truth values, or over the Boolean-valued truth functions.
Propositional formula
![About the simplest memory results when the output of an OR feeds back to one of its inputs, in this case output "q" feeding back into "p". The next simplest is the "flip-flop" shown below the once-flip. Analysis of these sorts of formulas can be done by either cutting the feedback path(s) or inserting (ideal) delay in the path. A cut path and an assumption that no delay occurs anywhere in the "circuit" results in inconsistencies for some of the '''total states''' (combination of inputs and outputs, e.g. (p=0, s=1, r=1) results in an inconsistency). When delay is present these inconsistencies are merely '''transient''' and expire when the delay(s) expire. The drawings on the right are called [[state diagram]]s.](https://commons.wikimedia.org/wiki/Special:FilePath/Propositional formula flip flops 1.png?width=200 "About the simplest memory results when the output of an OR feeds back to one of its inputs, in this case output \"q\" feeding back into \"p\". The next simplest is the \"flip-flop\" shown below the once-flip. Analysis of these sorts of formulas can be done by either cutting the feedback path(s) or inserting (ideal) delay in the path. A cut path and an assumption that no delay occurs anywhere in the \"circuit\" results in inconsistencies for some of the '''total states''' (combination of inputs and outputs, e.g. (p=0, s=1, r=1) results in an inconsistency). When delay is present these inconsistencies are merely '''transient''' and expire when the delay(s) expire. The drawings on the right are called [[state diagram]]s.")
TYPE OF LOGICAL FORMULA IN THE PROPOSITIONAL LOGIC
Sentential formula; Propositional form; Propositional expression; The map method; Propositional encoding
In propositional logic, a propositional formula is a type of syntactic formula which is well formed and has a truth value. If the values of all variables in a propositional formula are given, it determines a unique truth value.
Mathematical logic
SUBFIELD OF MATHEMATICS
Symbolic Logic; Symbolic logic; Mathematical Logic; Logic (mathematics); Logic (math); Logic (maths); Logic (symbolic); Mathematical logician; Logic modeling; Logic modelling; Formal Logic; History of mathematical logic; Subfields of mathematical logic; Formal logical systems; History of symbolic logic; Applications of mathematical logic; 20th century in mathematical logic
Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory.
Википедия
Propositional calculus
Propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. It deals with propositions (which can be true or false) and relations between propositions, including the construction of arguments based on them. Compound propositions are formed by connecting propositions by logical connectives. Propositions that contain no logical connectives are called atomic propositions.
Unlike first-order logic, propositional logic does not deal with non-logical objects, predicates about them, or quantifiers. However, all the machinery of propositional logic is included in first-order logic and higher-order logics. In this sense, propositional logic is the foundation of first-order logic and higher-order logic.
