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Style of formal logical argumentation
logic, sequent calculus is a style of formal logical argumentation in which every line of a proof is a conditional tautology (called a sequent by Gerhard
Sequent_calculus
Logical proof involving antecedents and consequents
In mathematical logic, a sequent is a very general kind of conditional assertion. A 1 , … , A m ⊢ B 1 , … , B n . {\displaystyle A_{1},\,\dots ,A_{m}\
Sequent
Disorder of decreased tolerance to specific sounds
Misophonia (or selective sound sensitivity syndrome) is a disorder of decreased tolerance to specific sounds or their associated stimuli, or cues. These
Misophonia
Topics referred to by the same term
Look up sequent in Wiktionary, the free dictionary. A sequent is a formalized statement of provability used within sequent calculus. Sequent may also refer
Sequent_(disambiguation)
In structural proof theory, the nested sequent calculus is a reformulation of the sequent calculus to allow deep inference. Alwen Tiu; Egor Ianovski; Rajeev
Nested_sequent_calculus
American computer hardware company
Sequent Computer Systems, Inc. was a computer company that designed and manufactured multiprocessing computer systems. They were among the pioneers in
Sequent_Computer_Systems
Operating system
DYNIX (DYNamic UnIX) was a Unix-like operating system developed by Sequent Computer Systems, based on 4.2BSD and modified to run on Intel-based symmetric
DYNIX
Theorem in formal logic
Hauptsatz) is the central result establishing the significance of the sequent calculus. It was originally proved by Gerhard Gentzen in part I of his
Cut-elimination_theorem
Kind of proof calculus
natural deduction. For this reason he introduced his alternative system, the sequent calculus, for which he proved the Hauptsatz both for classical and intuitionistic
Natural_deduction
System of resource-aware logic
intuitions. Proof-theoretically, it derives from an analysis of classical sequent calculus in which uses of (the structural rules) contraction and weakening
Linear_logic
1974 studio album by Tangerine Dream
soloing on a Mellotron which is treated by slowly sweeping filter effects. "Sequent C'" is a short piece by Peter Baumann on recorder, with tape echo. The
Phaedra_(album)
Method of deriving conclusions
underlying logical reasoning. Sequent calculi, another approach, introduce sequents as formal representations of arguments. A sequent has the form A 1 , … ,
Rule_of_inference
Rule of mathematical logic
is an inference rule of a sequent calculus that does not refer to any logical connective but instead operates on the sequents directly. Structural rules
Structural_rule
Subdiscipline of proof theory
proof theory comes from a technical notion introduced in the sequent calculus: the sequent calculus represents the assertion made at any stage of an inference
Structural_proof_theory
Algebraic manipulation of "true" and "false"
is sequent calculus, which has two sorts, propositions as in ordinary propositional calculus, and pairs of lists of propositions called sequents, such
Boolean_algebra
Topics referred to by the same term
Patent claim The assertion of a proposition; see Douglas N. Walton A right Sequent, in mathematics Another term for an advertising slogan Health claim A term
Claim
In sequent calculus, the completeness of atomic initial sequents states that initial sequents A ⊢ A (where A is an arbitrary formula) can be derived from
Completeness of atomic initial sequents
Completeness_of_atomic_initial_sequents
Relationship between programs and proofs
formulation of the isomorphism was referred to (a variant of) Gentzen's sequent calculus. The observation that the isomorphism is best understood with
Curry–Howard_correspondence
Branch of mathematical logic
analytic proof was introduced by Gentzen for the sequent calculus, where he proved that the sequent calculus of classical and intuitionistic logics are
Proof_theory
Less-restrictive form of modal logic
contains the congruence rule in its Hilbert calculus or the E rule in its sequent calculus upon the corresponding proof systems for classical propositional
Non-normal_modal_logic
Argument that leads to a logical absurdity
then P {\displaystyle P} may be concluded." In sequent calculus the principle is expressed by the sequent Γ , ¬ ¬ P ⊢ P , Δ {\displaystyle \Gamma ,\lnot
Reductio_ad_absurdum
Branch of logic
via natural deduction. The sequent calculus is a formal system that represents logical deductions as sequences or "sequents" of formulas. Developed by
Propositional_logic
Various systems of symbolic logic
Gerhard Gentzen discovered that a simple restriction of his system LK (his sequent calculus for classical logic) results in a system that is sound and complete
Intuitionistic_logic
emphasizes that CoS does not distinguish sequents and formulas, but uses a single object to do the job of both in a sequent calculus. Specifically, a structure
Calculus_of_structures
System of formal deduction in logic
changed in any of their rules of inference, while both natural deduction and sequent calculus contain some context-changing rules. Thus, if one is interested
Hilbert_system
German mathematician (1909–1945)
foundations of mathematics, proof theory, especially on natural deduction and sequent calculus. He died of starvation in a Czech prison camp in Prague in 1945
Gerhard_Gentzen
negative polarity. Many other sequent calculi has been shown to have the focusing property, notably the nested sequent calculi of both the classical and
Focused_proof
Branch of non-classical logic
significant substructural logics are relevance logic and linear logic. In a sequent calculus, one writes each line of a proof as Γ ⊢ Σ {\displaystyle \Gamma
Substructural_logic
Fundamental result of mathematical logic
Herbrand sequents, allowing Herbrand's theorem to be stated for sequents: "a Skolemized sequent is derivable if and only if it has a Herbrand sequent". Herbrand
Herbrand's_theorem
Branch of mathematics
{sq} _{p}(x)=\operatorname {cq} _{p}(x)^{p-1}.} The tanquent, cotanquent, sequent and cosequent functions can be defined as follows: tq p ( t ) = sq p
Squigonometry
American businessman
companies including Oden Technologies, OptConnect, Gatekeeper Systems, and Sequent Software. Thiel was born in France in a European-American household and
Fred_Thiel
Inference rule
In mathematical logic, the cut rule is an inference rule of sequent calculus. It is a generalisation of the classical modus ponens inference rule. The
Cut_rule
Type of logical system
sequent calculus was developed to study the properties of natural deduction systems. Instead of working with one formula at a time, it uses sequents,
First-order_logic
Computer memory design used in multiprocessing
Groupe Bull), Silicon Graphics (later Silicon Graphics International), Sequent Computer Systems (later IBM), Data General (later EMC, now Dell Technologies)
Non-uniform_memory_access
Mathematical logic concept
non- P {\displaystyle P} s." The transposition rule may be expressed as a sequent: ( P → Q ) ⊢ ( ¬ Q → ¬ P ) , {\displaystyle (P\to Q)\vdash (\neg Q\to \neg
Contraposition
1991 video game
Sequent was a DikuMUD derivative codebase developed by Raja Kushalnagar ("Duke of Sequent"). It was a text-based online role-playing game that was an
Sequent_(MUD)
to Australia only began in earnest after the discovery of gold and the sequent gold rushes in Australia. This migration shaped and influenced Australian
History of Chinese Australians
History_of_Chinese_Australians
Microsoft Unix operating system
system as an alternative for these. Unrelated to the later Dynix from Sequent Computer Systems Letwin, Gordon (1995-08-17). "What's happening to OS/2"
Xenix
German-born British philosopher (born 1960)
"Stoic Sequent Logic and Proof Theory", she argues that stoic deduction resembles backward proof search for Gentzen-style substructural sequent logics
Susanne_Bobzien
Property of many systems of logic
admissible. The weakening rule may be expressed as a natural deduction sequent: Γ ⊢ C Γ , A ⊢ C {\displaystyle {\frac {\Gamma \vdash C}{\Gamma ,A\vdash
Monotonicity_of_entailment
American Fortune 500 energy services holding company headquartered in Atlanta, Georgia
utilities, as well as for non-affiliated companies. Nicor Enerchange is Sequent Energy Management's Illinois- based brand for providing Commercial and
Southern_Company_Gas
British mathematician and logician
of St Andrews. He is known for his discovery in 1992 of a terminating sequent calculus for intuitionistic propositional logic. His Erdős number was 3
Roy_Dyckhoff
Rule of logical inference
placed on a subsequent line. The modus tollens rule may be written in sequent notation: P → Q , ¬ Q ⊢ ¬ P {\displaystyle P\to Q,\neg Q\vdash \neg P}
Modus_tollens
manufactured parallel computing systems. Together with Pyramid Technology and Sequent Computer Systems, Alliant's machines pioneered the symmetric multiprocessing
Alliant_Computer_Systems
2012 book by Nicholas J. Smith
proof trees, major variants of natural deduction, axiomatic proofs, and sequent calculus. It also includes numerous logical exercises. Paoli, F. (27 March
Logic:_The_Laws_of_Truth
Cirquent calculus (circuit sequent calculus) is a proof calculus that combines aspects of sequent calculus and boolean circuits. Its proof-objects are
Cirquent_calculus
Company Limited NSE: SELAN Selan Exploration Technology Limited NSE: SEQUENT Sequent Scientific Limited NSE: SERVOTECH Servotech Power Systems Limited NSE: SESHAPAPER
List of companies listed on the National Stock Exchange of India
List_of_companies_listed_on_the_National_Stock_Exchange_of_India
Topics referred to by the same term
chain (former NASDAQ ticker lk) System LK, in mathematics, the classical sequent calculus LK (spacecraft), a Soviet lunar lander LK (index mark code), county
LK
Mathematical problem
theory Formal proof Natural deduction Logical consequence Rule of inference Sequent calculus Theorem Systems axiomatic deductive Hilbert list Complete theory
Tarski's high school algebra problem
Tarski's_high_school_algebra_problem
Topics referred to by the same term
"assignor" in Assignment (law) In logic, the antecedent and succedent of a sequent in sequent calculus are called cedents. In insurance, a reinsured. This disambiguation
Cedent
1991 video game
1992 ~ 1994 1994 ~ Present TinyMUD AberMUD LPMud Farside AberMUD Diku Diku II Sequent Copper1 Copper2 Merc1 Copper2 Merc2 Farside/ AVATAR
AVATAR_MUD
Extension of linear logic
noncommutative multiplicative connectives of the Lambek calculus. Its sequent calculus relies on the structure of order varieties (a family of cyclic
Noncommutative_logic
Kind of non-classical logic
the premises relevant to the conclusion of the inference. Gentzen-style sequent calculi can be modified by removing the weakening rules that allow for
Relevance_logic
Theory that allows sets to be elements of themselves
theory Formal proof Natural deduction Logical consequence Rule of inference Sequent calculus Theorem Systems axiomatic deductive Hilbert list Complete theory
Non-well-founded_set_theory
Digital circuit without clock cycles
standing for "switching x on the background y" or "if x when y then") and sequention (with priority signs "xi≻xj" and "xi≺xj"). This takes into account not
Asynchronous_circuit
Subfield of mathematics
Hilbert-style deduction systems, systems of natural deduction, and the sequent calculus developed by Gentzen. The study of constructive mathematics, in
Mathematical_logic
Branch of mathematics
propositional calculus, Ricci calculus, calculus of variations, lambda calculus, sequent calculus, and process calculus. Furthermore, the term calculus has variously
Calculus
Symbol in mathematical logic
implies ⊢ {\displaystyle \vdash } ) In sequent calculus, the turnstile is used to denote a sequent. A sequent A 1 , … , A m ⊢ B 1 , … , B n {\displaystyle
Turnstile_(symbol)
Limitative results in mathematical logic
theory Formal proof Natural deduction Logical consequence Rule of inference Sequent calculus Theorem Systems axiomatic deductive Hilbert list Complete theory
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
Study of correct reasoning
There are different types of proof systems including natural deduction and sequent calculi. A semantics is a system for mapping expressions of a formal language
Logic
Subfield of automated reasoning and mathematical logic
theory Formal proof Natural deduction Logical consequence Rule of inference Sequent calculus Theorem Systems axiomatic deductive Hilbert list Complete theory
Automated_theorem_proving
U.S. federal court case about Linux use
obligated to recognize Novell's waiver of SCO's claims against IBM and Sequent". After the ruling Novell announced they have no interest in suing people
SCO Group, Inc. v. International Business Machines Corp.
SCO_Group,_Inc._v._International_Business_Machines_Corp.
theory Formal proof Natural deduction Logical consequence Rule of inference Sequent calculus Theorem Systems axiomatic deductive Hilbert list Complete theory
Decidability of first-order theories of the real numbers
Decidability_of_first-order_theories_of_the_real_numbers
Logical operation
theory Formal proof Natural deduction Logical consequence Rule of inference Sequent calculus Theorem Systems axiomatic deductive Hilbert list Complete theory
Negation
System of logic in mathematics and philosophy
three-valued Łukasiewicz logic was introduced by Arnon Avron in 1991. Sequent calculi for finite and infinite-valued Łukasiewicz logics as an extension
Łukasiewicz_logic
Function that preserves distinctness
theory Formal proof Natural deduction Logical consequence Rule of inference Sequent calculus Theorem Systems axiomatic deductive Hilbert list Complete theory
Injective_function
theory Formal proof Natural deduction Logical consequence Rule of inference Sequent calculus Theorem Systems axiomatic deductive Hilbert list Complete theory
Atomic model (mathematical logic)
Atomic_model_(mathematical_logic)
Approach to the semantics of logic that locates meaning in inferential role
developed through the analysis of Gerhard Gentzen's natural deduction and sequent calculus, through the Brouwer–Heyting–Kolmogorov interpretation of the
Proof-theoretic_semantics
Formal language used to prove statements
for radically different logics. For example, a paradigmatic case is the sequent calculus, which can be used to express the consequence relations of both
Proof_calculus
significance (omitting footnotes and most references): In the context of a sequent calculus such as G3c, special coherent implications as axioms can be converted
Geometric_logic
American television personality
software to Fortune 500 companies. A friend encouraged him to take a job with Sequent Computer Systems, which was headquartered in Beaverton, Oregon, in order
Matt_Roloff
Theorem in set theory
theory Formal proof Natural deduction Logical consequence Rule of inference Sequent calculus Theorem Systems axiomatic deductive Hilbert list Complete theory
Kőnig's_theorem_(set_theory)
Proof by Alan Turing
theory Formal proof Natural deduction Logical consequence Rule of inference Sequent calculus Theorem Systems axiomatic deductive Hilbert list Complete theory
Turing's_proof
Symbolic description of a mathematical object
theory Formal proof Natural deduction Logical consequence Rule of inference Sequent calculus Theorem Systems axiomatic deductive Hilbert list Complete theory
Expression_(mathematics)
Symbolic logic system
what is called an admissible rule of inference. His proof uses Gentzen's sequent calculus for intuitionistic logic. Weak forms of explosion prove the disjunctive
Minimal_logic
Topics referred to by the same term
Sequential manual transmission, an automotive transmission technology Sequention, a sequentional logic function Sequential (company), an American synthesizer
Sequential_(disambiguation)
Topics referred to by the same term
Proof calculus, a framework for expressing systems of logical inference Sequent calculus, a proof calculus for first-order logic Cirquent calculus, a proof
Calculus_(disambiguation)
Set of the elements not in a given subset
theory Formal proof Natural deduction Logical consequence Rule of inference Sequent calculus Theorem Systems axiomatic deductive Hilbert list Complete theory
Complement_(set_theory)
general idea in structural proof theory that breaks with the classical sequent calculus by generalising the notion of structure to permit inference to
Deep_inference
Complexity class used to classify decision problems
theory Formal proof Natural deduction Logical consequence Rule of inference Sequent calculus Theorem Systems axiomatic deductive Hilbert list Complete theory
NP_(complexity)
Theorem for proving more complex theorems
theory Formal proof Natural deduction Logical consequence Rule of inference Sequent calculus Theorem Systems axiomatic deductive Hilbert list Complete theory
Lemma_(mathematics)
Characteristic of some logical systems
theory Formal proof Natural deduction Logical consequence Rule of inference Sequent calculus Theorem Systems axiomatic deductive Hilbert list Complete theory
Completeness_(logic)
32-bit microprocessor
Opus532.32 Personal Mainframe – NS32032 PC Add-On Board PC532 – NS32532 Sequent Balance – NS32016, NS32032 and NS32332 multiprocessor Siemens PC-MX2 –
NS32000
Problem in computer science
theory Formal proof Natural deduction Logical consequence Rule of inference Sequent calculus Theorem Systems axiomatic deductive Hilbert list Complete theory
Halting_problem
Establishment of a theorem using inference from the axioms
sentence or determine that none exists. The concepts of Fitch-style proof, sequent calculus and natural deduction are generalizations of the concept of proof
Formal_proof
Rule of logical inference
argument using modus ponens is said to be deductive. In single-conclusion sequent calculi, modus ponens is the Cut rule. The cut-elimination theorem for
Modus_ponens
Logical connective OR
theory Formal proof Natural deduction Logical consequence Rule of inference Sequent calculus Theorem Systems axiomatic deductive Hilbert list Complete theory
Logical_disjunction
as various kinds of networks as opposed to the flat tree structures of sequent calculus. To distinguish the real proof nets from all the possible networks
Geometry_of_interaction
Yes-or-no question that cannot ever be solved by a computer
theory Formal proof Natural deduction Logical consequence Rule of inference Sequent calculus Theorem Systems axiomatic deductive Hilbert list Complete theory
Undecidable_problem
Type of search algorithm
functions are also called heuristic functions or branching heuristics. The sequent calculus-similar notation can be used to formalize many rewriting algorithms
DPLL_algorithm
Syllogism with conditional premise(s)
conditionals. The hypothetical syllogism inference rule may be written in sequent notation, which amounts to a specialization of the cut rule: P ⊢ Q Q ⊢
Hypothetical_syllogism
American software engineer (born 1978)
While in Oregon, he worked as an operating system developer, enhancing Sequent Computer Systems's DYNIX/ptx. In late 2000, Lattner joined the University
Chris_Lattner
Basic framework of mathematics
theory Formal proof Natural deduction Logical consequence Rule of inference Sequent calculus Theorem Systems axiomatic deductive Hilbert list Complete theory
Foundations_of_mathematics
Alternative to Tarskian semantics
theory Formal proof Natural deduction Logical consequence Rule of inference Sequent calculus Theorem Systems axiomatic deductive Hilbert list Complete theory
Truth-value_semantics
Type of cardinal number in mathematics
theory Formal proof Natural deduction Logical consequence Rule of inference Sequent calculus Theorem Systems axiomatic deductive Hilbert list Complete theory
Regular_cardinal
Nickname for the cluster of high-tech companies near Portland, USA
2001; Washington County campus closed in 2014) Sequent Computer Systems (purchased by IBM in 1993) Sequent, founded by a team that included three Intel
Silicon_Forest
Natural deduction Curry–Howard correspondence Cut-elimination theorem Sequent calculus Prawitz 1965. von Plato 2013, p. 85. Prawitz, Dag (1965). Natural
Normal form (natural deduction)
Normal_form_(natural_deduction)
On linear-time algorithms for graph logic
theory Formal proof Natural deduction Logical consequence Rule of inference Sequent calculus Theorem Systems axiomatic deductive Hilbert list Complete theory
Courcelle's_theorem
Equal sharing of all resources by multiple identical processors
systems were SMP. Early commercial Unix SMP implementations included the Sequent Computer Systems Balance 8000 (released in 1984) and Balance 21000 (released
Symmetric_multiprocessing
Concept in mathematical logic
theory Formal proof Natural deduction Logical consequence Rule of inference Sequent calculus Theorem Systems axiomatic deductive Hilbert list Complete theory
Functional_completeness
SEQUENT
SEQUENT
SEQUENT
SEQUENT
Boy/Male
Indian, Punjabi, Sikh
Elixir of Lord's Light
Girl/Female
Tamil
Girl/Female
Hindu, Indian, Marathi, Sanskrit
Consisting of Lightning; Shining; Glittering
Boy/Male
Hindu
The king of kings
Girl/Female
Hindu
Female
English
(Δάφνη) Greek name DAPHNE means "laurel." In mythology, this is the name of a nymph who was turned into a laurel tree by her father so that she might escape Apollo's unwanted attentions.
Male
Swiss
, Jehovah's gift, or, grace.
Boy/Male
Hindu
God
Girl/Female
Muslim
Elf friend, Highest, Height
Girl/Female
Arabic, Australian, Muslim
Smile
SEQUENT
SEQUENT
SEQUENT
SEQUENT
SEQUENT
n.
A follower.
a.
Following; succeeding; in continuance.
a.
Succeeding or following in order.
n.
The state of being sequent; succession; order of following; arrangement.
a.
Following as an effect; consequent.
n.
That which follows as a result; a sequence.