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Branch of logic
Propositional logic is a branch of classical logic. It is also called statement logic, sentential calculus, propositional calculus, sentential logic, or
Propositional_logic
Bearer of truth values
of its sensory nature, or as a propositional process whose contents can be true or false. Psychological propositionalism is the view that all intentional
Proposition
In logic, a statement which is always true
of propositional logic, or valid sentences of predicate logic that can be reduced to propositional tautologies by substitution. Propositional logic begins
Tautology_(logic)
Various systems of symbolic logic
Rocq. The syntax of formulas of intuitionistic logic is similar to propositional logic or first-order logic. However, intuitionistic connectives are not
Intuitionistic_logic
Method of deriving conclusions
Propositional logic is not concerned with the concrete meaning of propositions other than their truth values. Key rules of inference in propositional
Rule_of_inference
Study of correct reasoning
classical logic. It consists of propositional logic and first-order logic. Propositional logic only considers logical relations between full propositions. First-order
Logic
Assignment of meaning to the symbols of a formal language
for propositional logic consists of formulas built up from propositional symbols (also called sentential symbols, sentential variables, propositional variables)
Interpretation_(logic)
Type of logical system
from propositional logic, which does not use quantifiers or relations; in this sense, first-order logic is an extension of propositional logic. A theory
First-order_logic
System of formal deduction in logic
rule of inference – modus ponens, for propositional logics – or two – with generalisation, to handle predicate logics, as well – and several infinite axiom
Hilbert_system
Algebraic manipulation of "true" and "false"
language of propositional calculus, used when talking about propositional calculus) to denote propositions. The semantics of propositional logic rely on truth
Boolean_algebra
Class of formal logics
algebraic logic, it became apparent that classical propositional calculus admits other semantics. In Boolean-valued semantics (for classical propositional logic)
Classical_logic
Variable that can either be true or false
function. Propositional variables are the basic building-blocks of propositional formulas, used in propositional logic and higher-order logics. Formulas
Propositional_variable
Characteristic of some logical systems
propositional logic and first-order predicate logic are semantically complete, but not syntactically complete (for example, the propositional logic statement
Completeness_(logic)
In mathematics, a statement that has been proven
(e.g., non-classical logic). Although theorems can be written in a completely symbolic form (e.g., as propositions in propositional calculus), they are
Theorem
Type of formal logic
temporal logic include propositional dynamic logic (PDL), (propositional) linear temporal logic (LTL), computation tree logic (CTL), Hennessy–Milner logic, and
Modal_logic
2001 textbook by Graham Priest
introduction to non-classical propositional logics, which are logical systems that differ from standard classical propositional logic. It covers a wide range
An Introduction to Non-Classical Logic
An_Introduction_to_Non-Classical_Logic
Translation of a text into a logical system
For example, propositional logic only focuses on inferences based on logical connectives, like "and" or "if...then". First-order logic, on the other
Logic_translation
Symbol connecting formulas in logic
or negate arithmetic expressions. For instance, in the syntax of propositional logic, the binary connective ∨ {\displaystyle \lor } (meaning "or") can
Logical_connective
Logic formula
propositional logic, a propositional formula is a type of syntactic formula which is well formed. If the values of all variables in a propositional formula
Propositional_formula
Kind of proof calculus
specified – see § Propositional inference rules (Suppes–Lemmon style). This section defines the formal syntax for a propositional logic language, contrasting
Natural_deduction
Technique in mathematical logic
a set of propositional formulas and φ a propositional formula, then T ⊢ φ in classical logic if and only if T ⊢ ¬¬φ in intuitionistic logic. In particular
Double-negation_translation
Syntactically correct logical formula
are in propositional logic and predicate logic. A key use of formulas is in propositional logic and predicate logic such as first-order logic. In those
Well-formed_formula
Hilbert-style deductive systems for propositional logics. Classical propositional calculus is the standard propositional logic. Its intended semantics is bivalent
List of axiomatic systems in logic
List_of_axiomatic_systems_in_logic
Whether a decision problem has an effective method to derive the answer
effectively determined. Zeroth-order logic (propositional logic) is decidable, whereas first-order and higher-order logic are not. A theory (set of sentences
Decidability_(logic)
Logical principle
In logic, the law of excluded middle or the principle of excluded middle states that for every proposition, either this proposition or its negation is
Law_of_excluded_middle
Mathematical logic concept
In mathematical logic, an atomic formula (also known as an atom or a prime formula) is a formula with no deeper propositional structure, that is, a formula
Atomic_formula
System for reasoning about vagueness
mathematical logic, there are several formal systems of "fuzzy logic", most of which are in the family of t-norm fuzzy logics. The most important propositional fuzzy
Fuzzy_logic
Argument whose conclusion must be true if its premises are
In propositional logic, they are tautologies. A statement can be called valid, i.e. logical truth, in some systems of logic like in Modal logic if the
Validity_(logic)
Ancient philosophy
with Aristotelian term logic, the system of propositional logic developed by the Stoics was one of the two great systems of logic in the classical world
Stoicism
Overview of and topical guide to logic
logic Non-monotonic logic Ordered logic Paraconsistent logic Philosophical logic Predicate logic Propositional logic Provability logic Quantum logic Relevance
Outline_of_logic
Possessing negative truth value
classical propositional calculus, each proposition will be assigned a truth value of either true or false. Some systems of classical logic include dedicated
False_(logic)
System including an indeterminate value
propositional logic using the truth values {false, unknown, true}, and extends conventional Boolean connectives to a trivalent context. Boolean logic
Three-valued_logic
Rules used for constructing, or transforming the symbols and words of a language
Truth-functional propositional logic and first-order predicate logic are semantically complete, but not syntactically complete (for example the propositional logic statement
Syntax_(logic)
Property of a mathematical operation
the parentheses in an expression will not change the result. In propositional logic, associativity is a valid rule of replacement for expressions in
Associative_property
Propositional logic theorem
In propositional logic, the double negation of a statement states that "it is not the case that the statement is not true". In classical logic, every
Double_negation
Greek Stoic philosopher (c.279–c.206 BC)
Chrysippus excelled in logic, the theory of knowledge, ethics, and physics. He created an original system of propositional logic in order to better understand
Chrysippus
Formal systems of logic that significantly differ from standard logical systems
Non-classical logics (sometimes alternative logics) are formal systems that differ in a significant way from standard logical systems such as propositional and
Non-classical_logic
Concept in logic
in φ with (A ↔ A). In some deduction systems for propositional logic, a new expression (a proposition) may be entered on a line of a derivation if it is
Substitution_(logic)
Modal temporal logic with modalities referring to time
LTL is sometimes called propositional temporal logic (PTL). In terms of expressive power, LTL is a fragment of first-order logic. LTL was first proposed
Linear_temporal_logic
Function in logic
constant Modal operator Propositional calculus Truth-functional propositional logic Roy T. Cook (2009). A Dictionary of Philosophical Logic, p. 294: Truth Function
Truth_function
Form of logic that allows quantification over predicates
In logic and mathematics, second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. Second-order logic
Second-order_logic
Inference rule in logic, proof theory, and automated theorem proving
theorem-proving technique for sentences in propositional logic and first-order logic. For propositional logic, systematically applying the resolution rule
Resolution_(logic)
Rule of logical inference
In propositional logic, modus ponens (/ˈmoʊdəs ˈpoʊnɛnz/; MP), also known as modus ponendo ponens (from Latin 'mode that by affirming affirms'), implication
Modus_ponens
Type of propositional logic
second-order propositional logic is a propositional logic extended with quantification over propositions. A special case are the logics that allow second-order
Second-order propositional logic
Second-order_propositional_logic
Statement that is taken to be true
predicate logic more logical axioms than that are required, in order to prove logical truths that are not tautologies in the strict sense. In propositional logic
Axiom
Aspect of mathematical logic
most important achievement of abstract algebraic logic has been the classification of propositional logics in a hierarchy, called the abstract algebraic
Abstract_algebraic_logic
Symbol representing a property or relation in logic
true or false depending on those variables’ value or values. In propositional logic, atomic formulas are sometimes regarded as zero-place predicates
Predicate_(logic)
Propositional logic extending intuitionistic logic
mathematical logic, a superintuitionistic logic is a propositional logic extending intuitionistic logic. A logic is a set of propositional formulas with
Intermediate_logic
One of five systems of modal logic
book Symbolic Logic. It is a normal modal logic, and one of the oldest systems of modal logic of any kind. It is formed with propositional calculus formulas
S5_(modal_logic)
List of symbols used to express logical relations
contains logic symbols. Without proper rendering support, you may see question marks, boxes, or other symbols instead of logic symbols. In logic, a set
List_of_logic_symbols
Subfield of mathematics
Chrysippus, began the development of propositional logic. In 18th-century Europe, attempts to treat the operations of formal logic in a symbolic or algebraic way
Mathematical_logic
algebra and propositional logic. Algebra of sets Boolean algebra (structure) Boolean algebra Field of sets Logical connective Propositional calculus Ampheck
List of Boolean algebra topics
List_of_Boolean_algebra_topics
Logic theorem
principle of sufficient reason. The principle was stated as a theorem of propositional logic by Russell and Whitehead in Principia Mathematica as: ∗ 3 ⋅ 24 .
Law_of_noncontradiction
Pair of logical equivalences
In propositional logic and Boolean algebra, De Morgan's laws, also known as De Morgan's theorem, are a pair of transformation rules that are both valid
De_Morgan's_laws
Faulty deductive reasoning due to a logical flaw
in practice, "non sequitur" refers to an unnamed formal fallacy. Propositional logic is concerned with the meanings of sentences and the relationships
Formal_fallacy
Absorption is a valid argument form and rule of inference of propositional logic. The rule states that if P {\displaystyle P} implies Q {\displaystyle
Absorption_(logic)
Study of the scope and nature of logic
relation between logic and computer science arises from the parallels between propositional connectives of propositional logic and logic gates in computer
Philosophy_of_logic
Mathematical logic concept
truth-functional tautology or theorem of propositional logic. The principle was stated as a theorem of propositional logic by Russell and Whitehead in Principia
Contraposition
Family of formal knowledge representation
Description logics (DL) are a family of formal knowledge representation languages. Many DLs are more expressive than propositional logic but less expressive
Description_logic
Theory of logic to account for observations from quantum theory
quantum logic and some of these competitors, see § Relationship to other logics. Quantum logic has been proposed as the correct logic for propositional inference
Quantum_logic
Symbolic logic system
logic is usually formulated using the same syntax as intuitionistic propositional logic, with implication → {\displaystyle \to } , conjunction ∧ {\displaystyle
Minimal_logic
Tool for proving a logical formula
to the propositional case, with the additional assumption that free variables are considered universally quantified. As for the propositional case, formulae
Method_of_analytic_tableaux
Megarian-Stoic logic and Aristotelian logic is that Megarian-Stoic logic concerns propositions, not terms, and is thus closer to modern propositional logic. The
History_of_logic
Existence of values making formula true
respect to a fixed logic defining the syntax of allowed symbols, such as first-order logic, second-order logic or propositional logic. Rather than being
Satisfiability
Subfield of automated reasoning and mathematical logic
JOHNNIAC, the Logic Theorist constructed proofs from a small set of propositional axioms and three deduction rules: modus ponens, (propositional) variable
Automated_theorem_proving
Type of non-monotonic logic
between propositional default logic and the following logics have been studied: classical propositional logic; autoepistemic logic; propositional default
Default_logic
Reasoning about equations with free variables
(2011), "Propositional Consequence Relations and Algebraic Logic". Stanford Encyclopedia of Philosophy. Mainly about abstract algebraic logic. Stanley
Algebraic_logic
School of thought in philosophy of mathematics
B). Logicism also adopts from Frege's groundwork the reduction of natural language statements from "subject|predicate" into either propositional "atoms"
Logicism
3-volume treatise on mathematics, 1910–1913
σn) that can be thought of as the classes of propositional functions of τ1,...τm obtained from propositional functions of type (τ1,...,τm,σ1,...,σn) by
Principia_Mathematica
System for representing and reasoning about time
In logic, a temporal logic is any system of rules and symbolism for representing, and reasoning about, propositions qualified in terms of time (for example
Temporal_logic
Mathematical model for deduction or proof systems
arithmetic. Early logic systems includes Indian logic of Pāṇini, syllogistic logic of Aristotle, propositional logic of Stoicism, and Chinese logic of Gongsun
Formal_system
Type of formal logic
other logics avoid explosion: implicational propositional calculus, positive propositional calculus, equivalential calculus and minimal logic. The latter
Paraconsistent_logic
Application of logical methods to philosophical problems
classical logic, extended logics, and deviant logics. This classification is based on the idea that classical logic, i.e. propositional logic and first-order
Philosophical_logic
Study of the properties of logical systems
of truth-functional propositional logic (Paul Bernays 1918), (Emil Post 1920) Completeness of first-order monadic predicate logic (Leopold Löwenheim 1915)
Metalogic
Mathematical use of "there exists"
then, the negation of a propositional function's existential quantification is a universal quantification of that propositional function's negation; symbolically
Existential_quantification
propositional variable. This assignment can be uniquely extended to an assignment of truth values to all propositional formulas. In first-order logic
Valuation_(logic)
Computer science field
model-checking problem consists of verifying whether a formula in the propositional logic is satisfied by a given structure. Property checking is used for
Model_checking
can lead to a false one. A propositional fallacy is an error that concerns compound propositions. For a compound proposition to be true, the truth values
List_of_fallacies
Internet rage incitement technique
v t e Common fallacies (list) Formal In propositional logic Affirming a disjunct Affirming the consequent Conflation Denying the antecedent Argument from
Rage-baiting
placeholder in logical formulas. propositional logic The branch of logic that deals with propositions as units and uses propositional connectives to construct
Glossary_of_logic
Rule of logical inference
In propositional logic, modus tollens (/ˈmoʊdəs ˈtɒlɛnz/) (MT), also known as modus tollendo tollens (Latin for "mode that by denying denies") and denying
Modus_tollens
Mathematics notation with operators preceding operands
that names all 16 binary connectives of classical propositional logic. For classical propositional logic, it is a compatible extension of the notation of
Polish_notation
Concept in epistemology
A propositional attitude is a mental state held by an agent or organism toward a proposition. In philosophy, propositional attitudes can be considered
Propositional_attitude
Type of fallacious argument (logical fallacy)
In propositional logic, affirming the consequent (also known as converse error, fallacy of the converse, or confusion of necessity and sufficiency) is
Affirming_the_consequent
Type of logic regarding reasoning about beliefs
has a complete knowledge of propositional logic i.e., they sooner or later believe every tautology/theorem (any proposition provable by truth tables):
Doxastic_logic
Check the validity of a logic formula
checking the validity of a first-order logic formula using a resolution-based decision procedure for propositional logic. Since the set of valid first-order
Davis–Putnam_algorithm
Classical logic of two values, either true or false
classical logic is bivalent, but this is not true of every semantics for classical logic. In Boolean-valued semantics (for classical propositional logic), the
Principle_of_bivalence
In propositional calculus and proof complexity a propositional proof system (pps), also called a Cook–Reckhow propositional proof system, is a system for
Propositional_proof_system
Logical operation
In logic, negation, also called the logical not or logical complement, is an operation that takes a proposition P {\displaystyle P} to another proposition
Negation
System of logic in mathematics and philosophy
modal logic; it was later generalized to n-valued (for all finite integers n) as well as infinitely-many-valued (ℵ0-valued) variants, both propositional and
Łukasiewicz_logic
Approach to logic
In logic and formal semantics, term logic, also known as traditional logic, syllogistic logic or Aristotelian logic, is a loose name for an approach to
Term_logic
Formal system of logic
context. Zeroth-order logic (propositional logic) First-order logic Second-order logic Type theory Higher-order grammar Higher-order logic programming HOL (proof
Higher-order_logic
Logical rule of inference
salad. I will not choose soup. Therefore, I will choose salad. In propositional logic, disjunctive syllogism (also known as disjunction elimination and
Disjunctive_syllogism
Programming paradigm based on formal logic
possible ways, reducing it to a propositional logic program (known as grounding). Then they apply a propositional logic problem solver, such as the DPLL
Logic_programming
Device performing a Boolean function
ISBN 978-3-11022622-5. Büning, Hans Kleine; Lettmann, Theodor (1999). Propositional logic: deduction and algorithms. Cambridge University Press. p. 2. ISBN 978-0-521-63017-7
Logic_gate
Properties linking logical conjunction and disjunction
In propositional logic and Boolean algebra, there is a duality between conjunction and disjunction, also called the duality principle. It is the most
Conjunction/disjunction duality
Conjunction/disjunction_duality
Less-restrictive form of modal logic
propositional logic. Additional axioms, namely axioms M, C and N, can be added to form stronger logic systems. With all three axioms added to logic E
Non-normal_modal_logic
In mathematical logic, an atomic formula or its negation
these qualify as two separate occurrences. In propositional calculus a literal is simply a propositional variable or its negation. In predicate calculus
Literal_(mathematical_logic)
Type of informal fallacy
Argumentation scheme – Type of argument Argumentation theory – Academic field of logic and rhetoric Bait-and-switch – Form of fraud Straw man – Form of incorrect
Motte-and-bailey_fallacy
Extension of modal logic
simple propositional variables or atoms or compound propositions built with such logical connectives as and, or, and not. Propositional dynamic logic, or
Dynamic_logic_(modal_logic)
PROPOSITIONAL LOGIC
PROPOSITIONAL LOGIC
Surname or Lastname
English (of Norman origin)
English (of Norman origin) : habitational name from Déville in Seine-Maritime, France, probably named with Latin dei villa ‘settlement of (i.e. under the protection of) God’. This name was interpreted early on as a prepositional phrase de ville or de val and applied to dwellers in a town or valley (see Ville and Vale).English : nickname from Middle English devyle, Old English dēofol ‘devil’ (Latin diabolus, from Greek diabolos ‘slanderer’, ‘enemy’), referring to a mischievous youth or perhaps to someone who had acted the role of the Devil in a pageant or mystery play.French : variant of Ville, with the preposition de.
Girl/Female
Tamil
Trick, Power, Strategy, Solution by logic, By reasoning
Boy/Male
Hindu
Love and kindness, Analytical, Logical
Girl/Female
Gujarati, Hindu, Indian, Kannada, Tamil
Trick; Power; Strategy; Solution by Logic; By Reasoning
Boy/Male
Tamil
Intelligent, Logical
Boy/Male
Indian
Intelligent, Logical
Girl/Female
Tamil
Trick, Power, Strategy, Solution by logic, By reasoning
Girl/Female
Tamil
Vivikta | விவிகதா
Distinguished, Pure, Deep, Logically intelligent
Vivikta | விவிகதா
Girl/Female
Bengali, Hindu, Indian, Tamil, Telugu
Logically Intelligent; Who Stands Alone
Girl/Female
Hindu
Trick, Power, Strategy, Solution by logic, By reasoning
Girl/Female
Tamil
Viviktha | விவீகà¯à®¤à®¾Â
Distinguished, Pure, Deep, Logically intelligent
Viviktha | விவீகà¯à®¤à®¾Â
Boy/Male
Tamil
Love and kindness, Analytical, Logical
Girl/Female
Danish, Hindu, Indian, Japanese
Ray of Light; Logical
Boy/Male
Hindu
Full of feathers, Full of logic, Name of sage, Vatsyayan
Girl/Female
Indian
Successful; Logical Thinkers
Girl/Female
Hindu
Distinguished, Pure, Deep, Logically intelligent
Boy/Male
Hindu, Indian
Logical
Girl/Female
Hindu
Distinguished, Pure, Deep, Logically intelligent
Girl/Female
Arabic, Muslim, Pashtun
Logic; Reason
Boy/Male
Tamil
Full of feathers, Full of logic, Name of sage, Vatsyayan
PROPOSITIONAL LOGIC
PROPOSITIONAL LOGIC
Surname or Lastname
English
English : from the personal name Jack + the pejorative suffix -ard.
Boy/Male
Muslim
Wide, Vast, Spacious
Female
Swedish
Norwegian and Swedish form of Old Norse Yngvildr, YNGVILD means "Ing's warrior."
Girl/Female
Hindu
True image, Truth
Boy/Male
Indian
One who Spreads Love
Surname or Lastname
English
English : from an Old French personal name imported into England by the Normans in the forms Goscelin, Gosselin, Joscelin. For the most part it is from the Germanic personal name Gauzelin, a diminutive from a short form of the various compound names having as their first element the tribal name Gaut (apparently the same word as Old English GÄ“atas, the Scandinavian people to which Beowulf belonged, and also akin to the ethnic name Goth). However, the name also came to be considered as a pet form of Old French Josse (see Joyce).
Girl/Female
Hindu, Indian
Meaningful
Boy/Male
English
Great.
Surname or Lastname
English
English : apparently a topographic name for someone who lived where there was an abundance of thistles, from Middle English thistleProbably an Americanized form of German Distel.
Boy/Male
Indian, Punjabi, Sikh
Lovely and Attractive Lord
PROPOSITIONAL LOGIC
PROPOSITIONAL LOGIC
PROPOSITIONAL LOGIC
PROPOSITIONAL LOGIC
PROPOSITIONAL LOGIC
n.
A disjunctive proposition.
a.
Relating to, or securing, proportion.
a.
Pertaining to, or in the nature of, a proposition; considered as a proposition; as, a propositional sense.
a.
Constituting a proportion; having the same, or a constant, ratio; as, proportional quantities; momentum is proportional to quantity of matter.
a.
Having a due proportion, or comparative relation; being in suitable proportion or degree; as, the parts of an edifice are proportional.
n.
The part of a poem in which the author states the subject or matter of it.
n.
A proposition collected from the agreement of other previous propositions; any conclusion which results from reason or argument; inference.
n.
A disjunctive proposition.
n.
Any number or quantity in a proportion; as, a mean proportional.
a.
Following by necessary inference or rational deduction; as, a proposition consequent to other propositions.
n.
The inferred proposition of a syllogism; the necessary consequence of the conditions asserted in two related propositions called premises. See Syllogism.
a.
Capable of being proportioned, or made proportional; also, proportional; proportionate.
n.
A statement in terms of a truth to be demonstrated, or of an operation to be performed.
n.
A complete sentence, or part of a sentence consisting of a subject and predicate united by a copula; a thought expressed or propounded in language; a from of speech in which a predicate is affirmed or denied of a subject; as, snow is white.
n.
A statement of religious doctrine; an article of faith; creed; as, the propositions of Wyclif and Huss.
n.
The combining weight or equivalent of an element.
n.
A subaltern proposition.
n.
That which is offered or affirmed as the subject of the discourse; anything stated or affirmed for discussion or illustration.
n.
That which is proposed; that which is offered, as for consideration, acceptance, or adoption; a proposal; as, the enemy made propositions of peace; his proposition was not accepted.
a.
Of or pertaining to a preposition; of the nature of a preposition.