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Psychological theory
Propositional representation is the psychological theory, first developed in 1973 by Dr. Zenon Pylyshyn, that mental relationships between objects are
Propositional_representation
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
Branch of logic
Propositional logic is a branch of classical logic. It is also called statement logic, sentential calculus, propositional calculus, sentential logic,
Propositional_logic
Facts provided or learned about something or someone
meaning, understanding, mental stimuli, pattern, perception, proposition, representation, and entropy. Information is often processed iteratively: Data
Information
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
Boolean_algebra
Branch of mathematics that studies abstract algebraic structures
Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of
Representation_theory
State of mind
non-sensory states. Propositional attitudes are mental states that have propositional contents, in contrast to non-propositional states. Intentional states
Mental_state
Syntactically correct logical formula
Two key uses of formulas are in propositional logic and predicate logic. A key use of formulas is in propositional logic and predicate logic such as
Well-formed_formula
Amendment to California's Constitution
2025). "Sierra Club California Urges a Yes Vote on Proposition 50 to Protect Fair Representation". Sierra Club. Retrieved November 7, 2025. Sierra Club
2025 California Proposition 50
2025_California_Proposition_50
AI methods
A propositional model is compiled in an off-line phase in order to support some queries in polynomial time. Many ways of compiling a propositional model
Knowledge_compilation
Field of artificial intelligence
Knowledge representation (KR) aims to model information in a structured manner to formally represent it as knowledge in knowledge-based systems whereas
Knowledge representation and reasoning
Knowledge_representation_and_reasoning
System of formal deduction in logic
extend the propositional system to axiomatise classical predicate logic. Likewise, these three rules extend system for intuitionistic propositional logic (with
Hilbert_system
Diagram that shows all possible logical relations between a collection of sets
Venn in a paper entitled "On the Diagrammatic and Mechanical Representation of Propositions and Reasonings" in the Philosophical Magazine and Journal of
Venn_diagram
Mathematical table used in logic
logic—specifically in connection with Boolean algebra, Boolean functions, and propositional calculus—which sets out the functional values of logical expressions
Truth_table
British artist (born 1945)
"In this way, part of the object, becomes both material and propositional representation." This technique, (painting an image of an object, with ground
Amikam_Toren
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
Data structure for Boolean functions
structures include negation normal form (NNF), Zhegalkin polynomials, and propositional directed acyclic graphs (PDAG). A Boolean function can be represented
Binary_decision_diagram
1921 philosophical work by Ludwig Wittgenstein
of atomic propositions. Wittgenstein drew from Henry M. Sheffer's logical theorem making that statement in the context of the propositional calculus.
Tractatus Logico-Philosophicus
Tractatus_Logico-Philosophicus
About mathematical functions
yields a proposition; this proposition is called a "value" of the propositional function. In our example there are four values of the propositional function
History of the function concept
History_of_the_function_concept
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
Concept in Lie algebra representation theory
In the mathematical field of representation theory, the concept of weights of an algebra A over a field F is a generalisation of that of eigenvalues. They
Weight (representation theory)
Weight_(representation_theory)
Hypothetical internal cognitive symbol that represents external reality
A mental representation (or cognitive representation), in philosophy of mind, cognitive psychology, neuroscience, and cognitive science, is a hypothetical
Mental_representation
psycholinguistic studies on comprehension where a contrast between propositional representation and discourse model is made, and in neurolinguistic discourse
Discourse_grammar
Aspect of mathematical representation theory
In representation theory of Lie groups and Lie algebras, a fundamental representation is an irreducible finite-dimensional representation of a semisimple
Fundamental_representation
Inference rule in logic, proof theory, and automated theorem proving
refutation-complete theorem-proving technique for sentences in propositional logic and first-order logic. For propositional logic, systematically applying the resolution
Resolution_(logic)
Mathematical term
In mathematics, the adjoint representation (or adjoint action) of a Lie group G is a way of representing the elements of the group as linear transformations
Adjoint_representation
Logical incompatibility between two or more propositions
impossible?". In classical logic, particularly in propositional and first-order logic, a proposition φ {\displaystyle \varphi } is a contradiction if and
Contradiction
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
calculus is a logic and representation system defined by Ryszard S. Michalski. It combines elements of predicate logic, propositional calculus, and multi-valued
Attributional_calculus
referendum called for by former president Chirac. The 47th Proposition on proportional representation and on the inclusion of 30% of women on each electoral
110_Propositions_for_France
Awareness of facts, or competency
analytic philosophy. Propositional knowledge is propositional in the sense that it involves a relation to a proposition. Since propositions are often expressed
Knowledge
Type of formal logic
concurrent programs. Flavors of temporal logic include propositional dynamic logic (PDL), (propositional) linear temporal logic (LTL), computation tree logic
Modal_logic
Check the validity of a logic formula
first-order logic formula using a resolution-based decision procedure for propositional logic. Since the set of valid first-order formulas is recursively enumerable
Davis–Putnam_algorithm
Type of logical system
it from propositional logic, which does not use quantifiers or relations; in this sense, first-order logic is an extension of propositional logic. A
First-order_logic
Subfield of automated reasoning and mathematical logic
constructed proofs from a small set of propositional axioms and three deduction rules: modus ponens, (propositional) variable substitution, and the replacement
Automated_theorem_proving
Representation of a group or algebra that is a direct sum of simple representations
specifically in representation theory, a semisimple representation (also called a completely reducible representation) is a linear representation of a group
Semisimple_representation
Problem of determining if a Boolean formula could be made true
computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated SATISFIABILITY, SAT or B-SAT)
Boolean satisfiability problem
Boolean_satisfiability_problem
Philosophical study of knowledge
developed minds, such as humans, possess propositional knowledge. Propositional knowledge contrasts with non-propositional knowledge in the form of knowledge-how
Epistemology
A propositional directed acyclic graph (PDAG) is a data structure that is used to represent a Boolean function. A Boolean function can be represented
Propositional directed acyclic graph
Propositional_directed_acyclic_graph
Overview of and topical guide to logic
consequence Negation normal form Open sentence Propositional calculus Propositional formula Propositional variable Rule of inference Strict conditional
Outline_of_logic
Reasoning of knowledge about knowledge
autoepistemic logic is a formal logic for the representation and reasoning of knowledge about knowledge. While propositional logic can only express facts, autoepistemic
Autoepistemic_logic
Hypothesis of philosopher Jerry Fodor
theory of mind has to do with the relationship between propositional attitudes and representation. Dennett points out that a chess program can have the
Language of thought hypothesis
Language_of_thought_hypothesis
U.S. House districts in the state of California
California is the most populous U.S. state; as a result, it has the most representation in the United States House of Representatives, with 52 Representatives
California's congressional districts
California's_congressional_districts
Signs that stand in for and take the place of something else
Representation is the use of signs that stand in for and take the place of something else. It is through representation that people organize the world
Representation_(arts)
First case of a Lie group that is both compact and non-abelian
In the study of the representation theory of Lie groups, the study of representations of SU(2) is fundamental to the study of representations of semisimple
Representation theory of SU(2)
Representation_theory_of_SU(2)
Concept in mathematical group theory
mathematics, more specifically in group theory, the character of a group representation is a function on the group that associates to each group element the
Character_theory
Standard form of Boolean function
one or more literals. As in disjunctive normal form (DNF), the only propositional operators in CNF are or ( ∨ {\displaystyle \vee } ), and ( ∧ {\displaystyle
Conjunctive_normal_form
Complexity class used to classify decision problems
problem (SAT), where we want to know whether or not a certain formula in propositional logic with Boolean variables is true for some value of the variables
NP_(complexity)
Symbolic description of a mathematical object
software, the expressions are usually represented in this way. This representation is very flexible, and many things that seem not to be mathematical expressions
Expression_(mathematics)
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
Logical operation
that P → ⊥ {\displaystyle P\rightarrow \bot } . As a result, in the propositional case, a sentence is classically provable if its double negation is intuitionistically
Negation
Group representation
theoretical physics, a representation of a Lie group is a linear action of a Lie group on a vector space. Equivalently, a representation is a smooth homomorphism
Representation_of_a_Lie_group
used to refer to the representation of classical propositional logic as a vector space, in which the unit vectors are propositional variables. Predicate
Vector_logic
models for sets of propositional formulas are equivalent to each other. According to [Ferraris, 2005], the reduct of a propositional formula F {\displaystyle
Stable_model_semantics
Representation of the symmetry group of spacetime in special relativity
The development of the representation theory has historically followed the development of the more general theory of representation theory of semisimple
Representation theory of the Lorentz group
Representation_theory_of_the_Lorentz_group
Typographic symbol
value and single bars are used. Propositional truncation (a type former that truncates a type down to a mere proposition in homotopy type theory): for any
Vertical_bar
Framework for exploring meaning
In formal linguistics, discourse representation theory (DRT) is a framework for exploring meaning under a formal semantics approach. One of the main differences
Discourse representation theory
Discourse_representation_theory
logic is analogous to the relationship between Boolean algebras and propositional logic (see Lindenbaum–Tarski algebra). There are other ways to relate
Polyadic_algebra
Four-dimensional number system
} This representation has the following properties: Constraining any two of b, c, and d to zero produces a representation of complex numbers
Quaternion
Property of a mathematical operation
rearranging the parentheses in an expression will not change the result. In propositional logic, associativity is a valid rule of replacement for expressions
Associative_property
Concept in mathematics
In mathematics, a unitary representation of a group G is a linear representation π of G on a complex Hilbert space V such that π(g) is a unitary operator
Unitary_representation
Data organization and storage formats
decision diagram And-inverter graph Directed graph Directed acyclic graph Propositional directed acyclic graph Multigraph Hypergraph Lightmap Winged edge Quad-edge
List_of_data_structures
Map from algebra to geometric transforms
In the field of representation theory in mathematics, a projective representation of a group G on a vector space V over a field F is a group homomorphism
Projective_representation
Academic discipline
simply typed lambda calculus correspond to proofs of intuitionistic propositional logic. Category theory represents a view of mathematics that emphasizes
Logic_in_computer_science
Integers have unique prime factorizations
(the empty product corresponds to k = 0). This representation is called the canonical representation of n, or the standard form of n. For example, 999
Fundamental theorem of arithmetic
Fundamental_theorem_of_arithmetic
Statement that is taken to be true
prove logical truths that are not tautologies in the strict sense. In propositional logic, it is common to take as logical axioms all formulae of the following
Axiom
Ancient philosophy
Marcus Aurelius. Along with Aristotelian term logic, the system of propositional logic developed by the Stoics was one of the two great systems of logic
Stoicism
image-based and propositional accounts of cognition. Mental imagery is typically defined in psychology as a perceptual representation that is not directly
Imagery_debate
Graphical set representation involving overlapping shapes
table method precisely defined by Emil Post and the application of propositional logic to switching logic by (among others) Shannon, Stibitz, and Turing
Euler_diagram
Artificial intelligence algorithm
algorithm based on propositional logic. A Tsetlin machine is a form of learning automaton collective for learning patterns using propositional logic. Ole-Christoffer
Tsetlin_machine
American lawyer (born 1941)
, his unsuccessful representation of Democratic presidential candidate Al Gore in Bush v. Gore, and for successful representation of the plaintiff in
David_Boies
Prohairesis Property (ownership) Property (characteristic) Proposition Propositional attitude Propositional calculus Qualia Quality Quantity Quidditas Rasa Rajas
List of philosophical concepts
List_of_philosophical_concepts
Group of unitary complex matrices with determinant of 1
Lie bracket. Particle physicists often use a different, equivalent representation: The set of traceless Hermitian n × n complex matrices with Lie bracket
Special_unitary_group
Concept in mathematics
linear representation of a group G, then with the above linear action, the tensor algebra T ( V ) {\displaystyle T(V)} is an algebraic representation of G;
Tensor product of representations
Tensor_product_of_representations
Two types of knowledge, justification, or argument
justification, or argument by their reliance on experience. Roughly speaking, a proposition is known or justified a priori if it is known or justified independently
A_priori_and_a_posteriori
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
Theory of cognition
proposed an alternative method – the propositional theory – of how knowledge is mentally represented. The propositional theory claims that mental representations
Dual-coding_theory
Boolean algebra with unary operators expressing necessity and possibility modalities
x\land \Box y} for all x, y in A. Modal algebras provide models of propositional modal logics in the same way as Boolean algebras are models of classical
Modal_algebra
Computation model defining an abstract machine
(DFA) on a given real machine has quadrillions. This makes the DFA representation infeasible to analyze. Turing machines describe algorithms independent
Turing_machine
Correspondence in functional analysis
{\displaystyle *} -representation from the state. It is named for Israel Gelfand, Mark Naimark, and Irving Segal. A ∗ {\displaystyle *} -representation of a C ∗
Gelfand–Naimark–Segal construction
Gelfand–Naimark–Segal_construction
Subjective attitude that something is true
directed at: its object. Propositional attitudes are directed at propositions. Beliefs are usually distinguished from other propositional attitudes, like desires
Belief
is an isomorphism, then F is called a hull of G. Grothendieck (1960, proposition 3.1) showed that a functor from the category C of Artinian algebras to
Schlessinger's_theorem
Task in natural language processing
structured, machine-readable representation of the information in text, usually in the form of triples or n-ary propositions. A proposition can be understood as
Open_information_extraction
American conservative legal activist
Admissions v. Harvard lawsuits. Blum is the director of the Project on Fair Representation, which he founded in 2005 and operates alone. Blum was born in 1952
Edward_Blum_(activist)
Formulaic summary of Buddhist doctrines
most important teachings in Buddhism, they have both a symbolic and a propositional function. Symbolically, they represent the awakening and liberation
Four_Noble_Truths
Belarusian adventurer and self-declared King of Andorra (1896–1989)
1932, Skossyreff registered "Boris de Skossyreff: import - export, representation" in Santa Marta, Colombia. During this period, he was said to have learned
Boris_Skossyreff
Type of investigation
the realm of reasoning that is variously known as Boolean algebra, propositional calculus, sentential calculus, or zeroth-order logic. By way of approaching
Inquiry
American philosopher, logician, and computer scientist (born 1939)
influential papers on intensional semantics and propositional attitudes, including "A model theory for propositional attitudes" in Linguistics and Philosophy
Richmond_Thomason
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
Polish_notation
Programming language designed 1942 to 1945
existed and was known as propositional calculus. What Zuse had in mind, however, needed to be much more powerful (propositional calculus is not Turing-complete
Plankalkül
Reasoning about equations with free variables
Lewis in 1918. He treated the logic of relations as derived from the propositional functions of two or more variables. Hugh MacColl, Gottlob Frege, Giuseppe
Algebraic_logic
Beach, voted against Proposition 8. La Mesa was a virtual tie for the proposition, while Carlsbad only supported the proposition by a 2% margin. Percentage
Politics_of_San_Diego_County
Processing of natural language by a computer
intelligence. NLP is also related to information retrieval, knowledge representation, computational linguistics, and linguistics more broadly. Major processing
Natural_language_processing
Assumption that what is not known to be true is false
K {\displaystyle K} is also a model of K {\displaystyle K} ; in the propositional case, this condition is equivalent to K {\displaystyle K} having a single
Closed-world_assumption
Form of incorrect argument and informal fallacy
selection form focuses on a partial and weaker (and easier to refute) representation of the opponent's position. Then the easier refutation of this weaker
Straw_man
Strategic management template
a visual chart with elements describing a firm's or product's value proposition, infrastructure, customers, and finances, assisting businesses to align
Business_model_canvas
Process of changing beliefs to take into account a new piece of information
is instead not a compact representation of preference because the space required is exponential in the number of propositional letters. The complexity
Belief_revision
Representations of finite groups, particularly on vector spaces
The representation theory of groups is a part of mathematics which examines how groups act on given structures. Here the focus is in particular on operations
Representation theory of finite groups
Representation_theory_of_finite_groups
Belief merging, also called belief fusion or propositional belief merging, is a process in which an individual agent aggregates possibly conflicting pieces
Belief_merging
Problem in computer science
(P) and an input (x), does (P(x)) eventually halt? The conventional representation of decision problems is the set of objects possessing the property in
Halting_problem
PROPOSITIONAL REPRESENTATION
PROPOSITIONAL REPRESENTATION
Girl/Female
Hindu, Indian
Representation of Love
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.
PROPOSITIONAL REPRESENTATION
PROPOSITIONAL REPRESENTATION
Female
Native American
Native American Iroquois name ORENDA means "magic power."
Boy/Male
British, English, French, Latin
Fair; Righteous
Girl/Female
Hindu
Academic curiosity
Male
African
nature.
Boy/Male
Indian, Punjabi, Sikh
King's Victory; Victory of Land
Boy/Male
Tamil
Wise power
Boy/Male
Buddhist, Indian, Punjabi, Sanskrit, Sikh
Gold
Girl/Female
German, Latin
Wise Guardian; Form of Regina; Queen
Boy/Male
Muslim
Infallible. Innocent.
Boy/Male
Hindu, Indian, Mythological
Shiva's Son
PROPOSITIONAL REPRESENTATION
PROPOSITIONAL REPRESENTATION
PROPOSITIONAL REPRESENTATION
PROPOSITIONAL REPRESENTATION
PROPOSITIONAL REPRESENTATION
n.
A proposition collected from the agreement of other previous propositions; any conclusion which results from reason or argument; inference.
n.
The inferred proposition of a syllogism; the necessary consequence of the conditions asserted in two related propositions called premises. See Syllogism.
a.
Having a due proportion, or comparative relation; being in suitable proportion or degree; as, the parts of an edifice are proportional.
n.
The combining weight or equivalent of an element.
n.
A statement in terms of a truth to be demonstrated, or of an operation to be performed.
a.
Relating to, or securing, proportion.
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.
n.
A statement of religious doctrine; an article of faith; creed; as, the propositions of Wyclif and Huss.
a.
Constituting a proportion; having the same, or a constant, ratio; as, proportional quantities; momentum is proportional to quantity of matter.
n.
That which is offered or affirmed as the subject of the discourse; anything stated or affirmed for discussion or illustration.
n.
The part of a poem in which the author states the subject or matter of it.
n.
Any number or quantity in a proportion; as, a mean proportional.
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 disjunctive proposition.
n.
A subaltern proposition.
a.
Capable of being proportioned, or made proportional; also, proportional; proportionate.
a.
Following by necessary inference or rational deduction; as, a proposition consequent to other propositions.
a.
Pertaining to, or in the nature of, a proposition; considered as a proposition; as, a propositional sense.
n.
A disjunctive proposition.