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field of computer science, timed propositional temporal logic (TPTL) is an extension of propositional linear temporal logic (LTL) in which variables are
Timed propositional temporal logic
Timed_propositional_temporal_logic
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
Modal temporal logic with modalities referring to time
which additionally allows branching time and quantifiers. LTL is sometimes called propositional temporal logic (PTL). In terms of expressive power, LTL
Linear_temporal_logic
automaton, timed propositional temporal logic and clock temporal logic. They are also used in programs such as UPPAAL which implement timed automata. Generally
Clock_(model_checking)
Metric temporal logic (MTL) is a special case of temporal logic. It is an extension of temporal logic in which temporal operators are replaced by time-constrained
Metric_temporal_logic
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
temporal logic (also interval logic) is a temporal logic for representing both propositional and first-order logical reasoning about periods of time that
Interval_temporal_logic
Type of formal logic
Flavors of temporal logic include propositional dynamic logic (PDL), (propositional) linear temporal logic (LTL), computation tree logic (CTL), Hennessy–Milner
Modal_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
Application of logical methods to philosophical problems
Temporal logic formalizes temporal relations between propositions. This includes ideas like whether something is true at some time or all the time and
Philosophical_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
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)
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
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
Theory in computer science
satisfy the property. Computation tree logic belongs to a class of temporal logics that includes linear temporal logic (LTL). Although there are properties
Computation_tree_logic
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
checking needs to find a Büchi automaton (BA) equivalent to a given linear temporal logic (LTL) formula, i.e., such that the LTL formula and the BA recognize
Linear temporal logic to Büchi automaton
Linear_temporal_logic_to_Büchi_automaton
French theoretical computer scientist
logic, timed propositional temporal logic, over another, metric temporal logic.[G] Other topics in her research include the application of timed automata
Patricia_Bouyer-Decitre
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
Concept in model checking (computer science)
holds". Temporal logics such as linear temporal logic describe types of linear time properties using formulae. This article is about propositional linear-time
Linear_time_property
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
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
Branching-time logic that is a superset of LTL and CTL
tree logic (CTL) and linear temporal logic (LTL). It freely combines path quantifiers and temporal operators. Like CTL, CTL* is a branching-time logic. The
CTL*
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
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
Predicates over a system state. LTL: Linear temporal logic; a modal temporal logic with modalities referring to time. MCL: Model Checking Language; Alternation-Free
List_of_model_checking_tools
1943 paper proposing artificial neural networks
that these are equivalent. They considered "temporal propositional expressions" (TPE), which are propositional formulas with one free variable t {\displaystyle
A Logical Calculus of the Ideas Immanent in Nervous Activity
A_Logical_Calculus_of_the_Ideas_Immanent_in_Nervous_Activity
Field of philosophical and mathematical logic studying agency and action
logic was originally developed to reason about the behaviour of computer programs, treating program execution as a kind of action. In propositional dynamic
Agentive_logic
"Avicennian logic" as a replacement of Aristotelian logic. Avicenna's system of logic was responsible for the introduction of hypothetical syllogism, temporal modal
Logic_in_Islamic_philosophy
Statement that players know and also know that other players know (ad infinitum)
multi-modal logic systems in which the modal operators are interpreted epistemically. At the propositional level, such systems are extensions of propositional logic
Common_knowledge_(logic)
possible futures. Intuitively, it means that any timed propositional temporal logic-formula, or timed automaton or signal automaton using only the constraints
Region_(model_checking)
Complexity class
2-EXPTIME-complete. Implicational Relevance Logic is 2-EXPTIME-complete. The satisfiability problem for propositional dynamic logic with intersection (IPDL) is 2-EXPTIME-complete
2-EXPTIME
Computer science and logic conference
Miller, "A multiple-conclusion meta-logic" Igor Walukiewicz, "Completeness of Kozen's Axiomatisation of the Propositional Mu-Calculus" Parosh A. Abdulla,
Symposium on Logic in Computer Science
Symposium_on_Logic_in_Computer_Science
Hybrid logic refers to a number of extensions to propositional modal logic with more expressive power, though still less than first-order logic. In formal
Hybrid_logic
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
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
Family of modal logics for agency and choice
theory Agentive logic Deontic logic Dynamic logic (modal logic) Epistemic logic Branching time Coalition logic Alternating-time temporal logic Dynamic epistemic
STIT_logic
Philosophical descriptions of the temporal ordering of events
descriptions of the temporal ordering relation among events. The two series differ principally in their use of tense to describe the temporal relation between
A_series_and_B_series
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
Formal study of linguistic meaning
compound expression is determined by the meanings of its parts. Propositional and predicate logic are formal systems used to analyze the semantic structure
Formal semantics (natural language)
Formal_semantics_(natural_language)
an approach to temporal quantum logic developed by Chris Isham. It deals with the logical structure of quantum mechanical propositions asserted at different
HPO_formalism
Methods in artificial intelligence research
to first-order logic include temporal logic, to handle time; epistemic logic, to reason about agent knowledge; modal logic, to handle possibility and necessity;
Symbolic artificial intelligence
Symbolic_artificial_intelligence
Technique for symbolic model checking and logic calculi
concept of time for concurrency, state transition models are used. In particular, finite-state models can be used along with temporal logic in automatic
Counterexample-guided abstraction refinement
Counterexample-guided_abstraction_refinement
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
where S is the set of states of a state transition system. Linear temporal logic GOLOG Fluent calculus Situation calculus Event calculus Michael Gelfond
Action_language
Artificial intelligence 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
Type of software system
variations of propositional and symbolic (predicate) logic. These variations may be mathematically precise representations of formal logic systems (e.g
Reasoning_system
Branch of artificial intelligence
integer time. Temporal planning is closely related to scheduling problems when uncertainty is involved and can also be understood in terms of timed automata
Automated planning and scheduling
Automated_planning_and_scheduling
American philosopher (1930–2024)
and philosopher who has made contributions to the philosophy of logic, temporal logic, and structural proof theory. He taught at the University of Pittsburgh
Nuel_Belnap
Logician and philosopher (1914–1969)
Prior (1957) founded tense logic, now also known as temporal logic, and made important contributions to intensional logic, particularly in Prior (1971)
Arthur_Prior
1921 philosophical work by Ludwig Wittgenstein
bike) is not reducible to propositional knowledge according to Ryle, Wittgenstein also thought that the mastery of the logic of our language is a unique
Tractatus Logico-Philosophicus
Tractatus_Logico-Philosophicus
Emotional choice theory (also referred to as the "logic of affect") is a social scientific action model to explain human decision-making. Its foundation
Emotional_choice_theory
Theorem in temporal logic
In mathematical logic and computer science, Gabbay's separation theorem states that any formula in linear temporal logic (LTL) with past operators can
Gabbay's_separation_theorem
_{K}f\})\sim \lambda } . Computation tree logic Temporal logic Hansson, Hans, and Bengt Jonsson. "A logic for reasoning about time and reliability." Formal aspects
Probabilistic_CTL
Paradoxical assertion
In philosophy and logic, the classical liar paradox or liar's paradox or antinomy of the liar is the statement of a liar that they are lying: for instance
Liar_paradox
13th-century Medieval Persian Islamic scholar
most studied logic textbook of all time". Al-Katibi's logic was largely inspired by the formal Avicennian system of temporal modal logic, but is more
Najm al-Din al-Qazwini al-Katibi
Najm_al-Din_al-Qazwini_al-Katibi
Programming paradigm based on modeling the logic of a computation
science, declarative programming is a programming paradigm that expresses the logic of a computation without fully describing its control flow. The paradigm
Declarative_programming
boolean formulas First-order logic of equality Provability in intuitionistic propositional logic Satisfaction in modal logic S4 First-order theory of the
List of PSPACE-complete problems
List_of_PSPACE-complete_problems
Process of drawing correct inferences
specific domains. For example, modal logic can be used to reason about what is possible and what is necessary. Temporal logic can be used to draw inferences
Logical_reasoning
Ways how entities stand to each other
were treated in the field of logic before modern formal logic. For example, Aristotelian logic restricts itself to propositions in a subject-predicate form
Relation_(philosophy)
Basic proposition or assumption
principles are referred to as postulates by Kantians. In mathematics and formal logic, first principles are referred to as axioms or postulates. In physics and
First_principle
Italian philosopher and logician (1940–2025)
propositional attitude attributions, based on the idea of perspectivity: the systematic ambiguity of interpretation which characterizes propositional
Andrea_Bonomi_(philosopher)
Subfield of artificial intelligence
use of symbols included non-trivial logic and, if it did, whether the logic was propositional or first-order logic. This categorization is compared with
Neuro-symbolic_AI
Statements involving superpositions of truth
modal logic. Springer. pp. 35–40. ISBN 978-0-7923-5335-5. attempts to reconstruct both Aristotle's and Diodorus' arguments in propositional modal logic Dorothea
Problem_of_future_contingents
Idea that refutes itself
tolerant logics (e.g. paraconsistent logics and direct logic) that lack proof by contradiction. For example, the negation of a proposition can be proved
Self-refuting_idea
Argument that uses faulty reasoning
meaningful propositions. Logical form alone can guarantee that, given true premises, a true conclusion must follow. However, formal logic makes no such
Fallacy
Computational Formula that can be measured in terms of True or False
Boolean formula is a formula in quantified propositional logic (also known as Second-order propositional logic) where every variable is quantified (or bound)
True quantified Boolean formula
True_quantified_Boolean_formula
List of concepts in artificial intelligence
relations. propositional calculus A branch of logic which deals with propositions (which can be true or false) and argument flow. Compound propositions are formed
Glossary of artificial intelligence
Glossary_of_artificial_intelligence
Topics referred to by the same term
an informal fallacy in which a proposition is repeatedly restated Time of assertion, in linguistics a secondary temporal reference in establishing tense
Assertion
Information science by discipline
formalisms have been used, including propositional and predicate calculi; deontic, temporal and non-monotonic logics; and state transition diagrams. Prakken
Legal_informatics
List of statements that appear to contradict themselves
travel, information or objects appear to have no beginning. Temporal paradox: What happens if a time traveler alters the past in a way that prevents their actions
List_of_paradoxes
Process of changing beliefs to take into account a new piece of information
exponential in the number of propositional letters. The complexity of query answering and model checking in the propositional case is in the second level
Belief_revision
American philosopher and logician (1940–2022)
the propositional modal logic must be weakened. Kripke semantics for intuitionistic logic follows the same principles as the semantics of modal logic, but
Saul_Kripke
logic Propositional logic First-order logic Second-order logic Higher-order logic Non-classical logic Description logic Digital logic Fuzzy logic Intuitionistic
Outline_of_philosophy
Name which is taken to uniquely identify its referent in the world
based on truth values and propositional logic, when trying to ascertain the criteria with which to determine if propositions that include proper names
Proper_name_(philosophy)
Metaphysical dependence relation between facts or entities
critique, see e.g. Thompson (2016) & Tallant, J. (2015), “What is Time? What is a Temporal Property?” American Philosophical Quarterly 52(4): 315–332. Schaffer
Metaphysical_grounding
Field of artificial intelligence
systems easier to design and build. KRR also incorporates findings from logic to automate various kinds of reasoning. Traditional KRR focuses more on
Knowledge representation and reasoning
Knowledge_representation_and_reasoning
Method of reasoning and philosophical argument
Hellenistic period, the Stoics integrated dialectic into logic as the study of argumentation and propositional structure, while Skeptics used it to suspend judgment
Dialectic
Mathematical theory of information underlying situation semantics
underlying ontology and logic that make such analyses precise, including the distinction between information, representations and propositions, and the treatment
Situation_theory
Concept in metaphysics and philosophy
axioms have not yet been stated for the temporal or spatial use of CT.) Let CT be stated in quantificational logic and contain the following primitives:[citation
Counterpart_theory
View that neither the future nor the past exist, only the present
do not exist now. Presentism is a view about temporal ontology, i.e., a view about what exists in time, that contrasts with eternalism—the view that
Philosophical_presentism
Austrian-German philosopher (1859–1938)
forms of true judgments. He includes here syllogistic classic logic, propositional logic, and that of predicates. This is a semantic stratum, and the rules
Edmund_Husserl
Version of modal realism
to how a particular moment or point in time is an index in the temporal dimension. The analogy to space and time is often used to convey this different
Extended_modal_realism
1781 book by Immanuel Kant
space and time rejects both the space and time of Aristotelian physics and the space and time of Newtonian physics. In the Transcendental Logic, there is
Critique_of_Pure_Reason
of artificial intelligence and computational logic. As an example of a method based on propositional logic, we can mention SLAF (Simultaneous Learning
Action_model_learning
Declarative logic programming language
is P-complete. The proof is based on Datalog metainterpreter for propositional logic programs. With respect to program complexity, the decision problem
Datalog
Philosophical tradition in Muslim culture
"Avicennian logic" as a replacement of Aristotelian logic. Avicenna's system of logic was responsible for the introduction of hypothetical syllogism, temporal modal
Islamic_philosophy
developments in Aristotelian logic, as well as innovations in non-Aristotelian temporal modal logic and inductive logic; and developments in research
Early_Islamic_philosophy
Planning programming language
It introduces non-propositional state-variables (which may be n-ary: true, false, unknown, or anything else). It introduces a temporal model given with
Planning Domain Definition Language
Planning_Domain_Definition_Language
Philosophical school
status. There are no 'levels' of reality. (2) All situations have a propositional form — that is, all situations have the form of "A is B". (3) Reality
Australian_realism
Scientific and philosophical encyclopedia by Avicenna
syllogism and on the propositional calculus, which were both part of the Stoic logical tradition. He developed an original theory of “temporally modalized” syllogistic
The_Book_of_Healing
Philosophical term
not made out of durationless instants, but ever smaller temporal intervals. Every interval of time can be divided into smaller and smaller intervals, without
Gunk_(mereology)
Conditionals that discuss what would have been if things were otherwise
central topics in philosophical logic, formal semantics, and philosophy of language. In particular, several conditional logics have been developed specifically
Counterfactual_conditional
Capacity for consciously making sense of things
Reason is the capacity to consciously apply logic by drawing valid conclusions from new or existing information, with the aim of seeking truth. It is
Reason
"the horse" can be considered to be the product of a propositional function. A propositional function is an operation of language that takes an entity
Philosophy_of_language
Academic field of logic and rhetoric
undermined by premises through logical reasoning. With historical origins in logic, dialectic and rhetoric, argumentation theory includes the arts and sciences
Argumentation_theory
Persian polymath, physician and philosopher (c. 980–1037)
early formal system of temporal logic was studied by Avicenna. Although he did not develop a real theory of temporal propositions, he did study the relationship
Avicenna
Issue in artificial intelligence and categorical algebra
"Non-monotonic Temporal Reasoning". In Gabbay, D. M.; Hogger, C. J.; Robinson, J. A. (eds.). Handbook of Logic in Artificial Intelligence and Logic Programming
Frame_problem
Intelligence of machines
trails). Formal logic is used for reasoning and knowledge representation. Formal logic comes in two main forms: propositional logic (which operates on
Artificial_intelligence
Uniqueness of countable dense linear orders
application of Cantor's isomorphism theorem involves temporal logic, a method for using logic to reason about time. In this application, the theorem implies that
Cantor's_isomorphism_theorem
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