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Type of formal logic
Paraconsistent logic is a type of non-classical logic that allows for the coexistence of contradictory statements without leading to a logical explosion
Paraconsistent_logic
Method of deriving conclusions
would lead to a contradiction. Paraconsistent logics revise classical logic to allow the existence of contradictions. In logic, a contradiction happens if
Rule_of_inference
Brazilian logician
interpretation for paraconsistent logics) contributed to a revival in the philosophical interpretation of paraconsistent logics. The logics of formal inconsistency
Walter_Carnielli
Theorem in formal logic
(P\wedge \lnot P)} . Paraconsistent logics have been developed that allow for subcontrary-forming operators. Model-theoretic paraconsistent logicians often
Principle_of_explosion
Logic theorem
trivialism. The law is employed in a reductio ad absurdum proof. Paraconsistent logics are those logics which deny explosion. Early in philosophy, it is hard to
Law_of_noncontradiction
Logical principles
also many valued logics, with gaps or gluts, or both. Intuitionistic logic denies the law of excluded middle. Paraconsistent logic tolerates contradiction
Law_of_thought
Symbolic logic system
Johansson under the name "Minimalkalkül". It is a paraconsistent logic weaker than intuitionistic logic that rejects the principle of explosion (ex falso
Minimal_logic
Application of logical methods to philosophical problems
principle of explosion found in classical logic. Relevance logic is a prominent form of paraconsistent logic. It rejects the purely truth-functional interpretation
Philosophical_logic
mathematics (e.g. analysis) based on a foundation of paraconsistent logic instead of classical logic. A number of reformulations of analysis can be developed
Paraconsistent_mathematics
System including an indeterminate value
the monoid identity. This logic is equivalent to an "ideal" paraconsistent logic which also obeys the contrapositive. The logic of here and there (HT, also
Three-valued_logic
British philosopher, born 1948
and liar paradoxes), and his many writings related to paraconsistent and other non-classical logics. In these he draws on the history of philosophy, including
Graham_Priest
View that there are statements that are both true and false
paraconsistent logics. Dialetheists who do not want to allow that every statement is true are free to favour these over traditional, explosive logics
Dialetheism
Kind of non-classical logic
side of the sequents. A notable feature of relevance logics is that they are paraconsistent logics: the existence of a contradiction will not necessarily
Relevance_logic
Various systems of symbolic logic
Intuitionistic logic is related by duality to a paraconsistent logic known as Brazilian, anti-intuitionistic or dual-intuitionistic logic. The subsystem
Intuitionistic_logic
Non-contradiction of a theory
Łukasiewicz – Polish logician and philosopher (1878–1956) Paraconsistent logic – Type of formal logic ω-consistency – Mathematical theoryPages displaying short
Consistency
Logical operation
these ideas work in both classical and intuitionistic logic, they do not work in paraconsistent logic, where contradictions are not necessarily false. As
Negation
Doctrine of multiplicity in contrast with monism
than one correct logic. Such as using classical logic in most cases, but using paraconsistent logic to deal with certain paradoxes. Metaphysical pluralism
Pluralism_(philosophy)
System of laws of thought
violate the law of contradiction of formal logic, although attempts have been made to create a paraconsistent logic. Some Soviet philosophers argued that the
Dialectical_logic
Brazilian philosopher and mathematician (1929–2024)
philosopher, best known for establishing and pioneering the field of paraconsistent logic. Born in Curitiba, he studied engineering and mathematics at the
Newton_da_Costa
Limitative results in mathematical logic
usually studied in the context of classical logic, they also have a role in the study of paraconsistent logic and of inherently contradictory statements
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
Study of correct reasoning
logics are multivalued logics that have an infinite number of "degrees of truth", represented by a real number between 0 and 1. Paraconsistent logics
Logic
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
Formal systems of logic that significantly differ from standard logical systems
of De Morgan's laws; Linear logic rejects idempotency of entailment as well; Paraconsistent logic (e.g., relevance logic) rejects the principle of explosion
Non-classical_logic
System for reasoning about vagueness
element Noise-based logic Paraconsistent logic Rough set Sorites paradox Trinary logic Type-2 fuzzy sets and systems Vector logic Novák, V.; Perfilieva
Fuzzy_logic
B)\equiv (C\equiv B))\equiv C)} Paraconsistent logic § Included — a list of axiom schemas for a paraconsistent logic of the Hilbert style Yasuyuki Imai
List of axiomatic systems in logic
List_of_axiomatic_systems_in_logic
contemporary logicians as a precursor to multi-valued logic, fuzzy logic, and paraconsistent logic. It has also been cited in discussions of relativism
Jaina_seven-valued_logic
Logical rule of inference
holds in classical propositional logic and intuitionistic logic, but not in some paraconsistent logics. Stoic logic Types of syllogism Copi, Irving M
Disjunctive_syllogism
Logical incompatibility between two or more propositions
noncontradiction – Logic theorem On Contradiction – 1937 essay by Mao Zedong Oxymoron – Figure of speech Paraconsistent logic – Type of formal logic Paradox –
Contradiction
Inference introducing a disjunction in logical proofs
paraconsistent logics because in combination with other rules of logic, it leads to explosion (i.e. everything becomes provable) and paraconsistent logic
Disjunction_introduction
Development of Indian logic
connective Dialetheism Paraconsistent logic Prasangika Two-truths doctrine Tarka-Sangraha Debates in ancient India Seven valued logic Gillon, Brendan (2024)
Indian_logic
Ancient Greek philosopher (fl. c. 500 BC)
1017/S0031819100048063. Priest, G., Sylvan, R., Norman, J., Arruda, A. I. (1989). Paraconsistent Logic: Essays on the Inconsistent. Austria: Philosophia. p .5 Lukasiewicz
Heraclitus
Polish logician and philosopher
Gerhard Gentzen in the 1930s. He is also known for his research into paraconsistent logic. He was the President (rector) of the Nicolaus Copernicus University
Stanisław_Jaśkowski
Concept in Nineteen Eighty-Four of accepting two contradictory statements
lie Contradiction Dissociation (psychology) Double-talk Hypocrisy Paraconsistent logic Political hypocrisy Reality-based community You can't have your cake
Doublethink
Formalisation of dialectic
1980s). One can include works of the communities of informal logic and paraconsistent logic. Building on theories of defeasible reasoning (see John L. Pollock)
Logic_and_dialectic
Method in artificial intelligence
reasoning Dialogical logic Logic and dialectic Logic of argumentation Knowledge representation and reasoning Paraconsistent logic Probabilistic argumentation
Argumentation_framework
Many-valued logic Modal logic Alethic logic Deontic logic Doxastic logic Epistemic logic Temporal logic Paraconsistent logic Substructural logic Metalogic
Outline_of_philosophy
Brazilian mathematical logician
Brazilian Logic Society. Topics in her work have included non-classical logic, paraconsistent logic, many-valued logic, and the history of logic. After graduating
Itala_D'Ottaviano
Formal logic whose entailment relation is not monotonic
new belief makes any logic for belief revision non-monotonic. The belief revision approach is alternative to paraconsistent logics, which tolerate inconsistency
Non-monotonic_logic
Logical theory
considered by some to be the complete opposite of radical skepticism. Paraconsistent logics may use "the law of non-triviality" to abstain from trivialism in
Trivialism
Process of drawing correct inferences
elimination while paraconsistent logics reject the principle of explosion. Deductive reasoning plays a central role in formal logic and mathematics. In
Logical_reasoning
Russian mathematician (1880–1940)
philosopher, psychologist, poet. He was a forerunner of paraconsistent and multi-valued logics. Vasiliev was born on June 29 O.S., 1880 in Kazan, Russia
Nicolai_A._Vasiliev
Belgian logician and epistemologist (born 1944)
and paraconsistent logics, his epistemological views may be broadly characterized as fallibilist. adaptive logics, paraconsistency, classical logic, content
Diderik_Batens
Logically self-contradictory statement
antinomy. In logic, it is often assumed, following Aristotle, that no dialetheia exist, but they are allowed in some paraconsistent logics. Frank Ramsey
Paradox
Field of philosophical logic
deontic logic have been developed, including non-monotonic deontic logics (e.g., Horty's prioritised default logic), paraconsistent deontic logics, dynamic
Deontic_logic
Peruvian philosopher (1918–2019)
public results. He was interested in so-called "unorthodox logics". The term "paraconsistent logic" was coined in 1976 by him. He was the first person of
Francisco Miró Quesada Cantuarias
Francisco_Miró_Quesada_Cantuarias
Branch of mathematics
incorporates choice sequences. Paraconsistent analysis, which is built upon a foundation of paraconsistent, rather than classical, logic and set theory. Smooth
Mathematical_analysis
Topics referred to by the same term
to -44 deg. See Star catalogue#Proper motion catalogues Logic of Paradox, a paraconsistent logic LP record, a long-playing 12- or 10-inch (30 or 25 cm)
LP
Logician
needed] Béziau works in the field of logic—in particular, paraconsistent logic, the square of opposition and universal logic. He holds a Maîtrise in Philosophy
Jean-Yves_Béziau
American philosopher (1928–2024)
implication); Rescher–Manor consequence relation Paraconsistent logic: Rescher–Brandom semantics Temporal logic: Rescher operator Scientometrics: Rescher's
Nicholas_Rescher
infrastructure of mathematics based on a foundation of paraconsistent logic instead of classical logic. Partition theory Perturbation theory Picard–Vessiot
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Class of non-classical logics
nonclassical logics in the past two decades—paraconsistent logics, linear logics, substructural logics, nonmonotonic logics, innumerable other logics for AI
Deviant_logic
Kind of proof calculus
Hendricks 2018, p. 38. Bostock 1997, p. 21. This is required in paraconsistent logics that do not treat ¬ {\displaystyle \neg } and ( ϕ → ⊥ ) {\displaystyle
Natural_deduction
New Zealand–born philosopher
Paraconsistent Logic: Essays on the Inconsistent, München: Philosophia Verlag. See Routley, Richard and Meyer, Robert K. (1976), "Dialectical Logic,
Richard_Sylvan
Addition to a theory to prevent falsification
Scientific Revolutions Proofs and Refutations "The Dragon in My Garage" Paraconsistent logic Moving the goalposts Stanovich, Keith E. (2007). How to Think Straight
Ad_hoc_hypothesis
non-normal) modal logic, hybrid logic, first-order modal logic, paraconsistent logic, linear logic, relevance logic, connexive logic, belief revision,
Dialogical_logic
Claim that human mathematicians are not describable as formal proof systems
inconsistent Turing Machine that could be reasoning using some sort of paraconsistent logic. Gödel himself commented about this disjunction in 1953. Penrose
Penrose–Lucas_argument
Method of reasoning via argumentation and contradiction
1980s). One can include works of the communities of informal logic and paraconsistent logic. Building on theories of defeasible reasoning (see John L. Pollock)
Dialectic
Spanish philosopher and lawyer
supervision, he wrote his dissertation on a system of contradictorial (paraconsistent) logic. At that time he was also granted a complementary degree in American
Lorenzo_Peña
Paradoxical assertion
dialetheists nearly always reject the explosion principle. Logics that reject it are called paraconsistent. Andrew Irvine has argued in favour of a non-cognitivist
Liar_paradox
Polish logician and ontologist
contributions are to the development of modal logic, paraconsistent logic and ontology. Ontologies and ontologics. In: Logic counts. Edited by Zarnecka-Bialy Ewa
Jerzy_Perzanowski
Logical proof involving antecedents and consequents
Similarly, one can obtain calculi for dual-intuitionistic logic (a type of paraconsistent logic) by requiring that sequents be singular in the antecedent
Sequent
American computer scientist; Planner programming language designer (1944–2022)
systems, organizational and multi-agent systems, logic programming, concurrent programming, paraconsistent logic and cloud computing. The Planner language was
Carl_Hewitt
Concept in philosophical logic
including as a model of traditional logic, quantifications, modal logic, order theory, or paraconsistent logic. For instance, the statement A may be
Logical_hexagon
Paradox introduced by David Makinson
pp. 232-254. (Minneapolis: University of Minnesota Press, 1983). Priest, Graham; Tanaka, Koji; Weber, Zach (24 September 1996). "Paraconsistent Logic".
Preface_paradox
Whether a decision problem has an effective method to derive the answer
are several basic results about decidability of theories. Every (non-paraconsistent) inconsistent theory is decidable, as every formula in the signature
Decidability_(logic)
Many-valued logic in which truth values comprise a continuous range
useful in systems of paraconsistent logic. If practical applications were to arise for such systems, multidimensional infinite-valued logic could develop as
Infinite-valued_logic
(1929–2024), mathematician and logician, recognised for his works in paraconsistent logic Oswaldo Cruz (1872–1917), physician and public health champion, eliminated
List_of_Brazilians
number, allowing pairs to be encoded as single values. paraconsistent logic A non-classical logic that allows for contradictions to exist without deriving
Glossary_of_logic
Logic System in India
Indian philosophy De Morgan's laws Dialetheism Logical connective Paraconsistent logic Prasangika Pyrrhonism Semiotic square Two-truths doctrine Sharana
Tetralemma
logic Causes and effects causal calculus – How one process influences another Knowledge about knowledge Belief revision Modal logics paraconsistent logics
Outline of artificial intelligence
Outline_of_artificial_intelligence
National University 1983. Reprinted as the introductory chapters of Paraconsistent Logic, G.Priest, R. Routley and J. Norman (eds.), Philosophia Verlag, 1989
Graham_Priest_bibliography
Varying application boundaries
information Many-valued logic Multiset Neuro-fuzzy Non-well-founded set theory Obfuscation Opaque context Paraconsistent logic Phenomenology (psychology)
Fuzzy_concept
Fourfold logical system in Indian philosophy
Philosophy portal Dialetheism Logical connective Paraconsistent logic Prasangika Semiotic square Term logic Tetralemma Two-truths doctrine Jayatilleke 1967
Catuṣkoṭi
German-Iranian philosopher of medicine
classical two-valued logic, many-valued logic, paraconsistent logic, deontic logic, temporal logic, probability logic, fuzzy logic, and so on. Their number
Kazem_Sadegh-Zadeh
Argentine logician
(2018). "Introducing consistency in a dialogical framework for paraconsistent logic" (PDF). Logic Journal of the IGPL. 28 (5): 953–972. doi:10.1093/jigpal/jzy069
Eduardo_Barrio
American philosopher (1930–2024)
logic provides a basis for paraconsistent logic to avoid this pathology of two-valued logic. In 1976 Belnap and T. B. Steel Jr. published The Logic of
Nuel_Belnap
Idea that refutes itself
an important role in some inconsistency tolerant logics (e.g. paraconsistent logics and direct logic) that lack proof by contradiction. For example, the
Self-refuting_idea
2012 book by Mark Colyvan
this mapping account. Chapter 7 explores issues surrounding paraconsistent mathematics and logic. Colyvan argues that mathematical theory can be inconsistent
An Introduction to the Philosophy of Mathematics
An_Introduction_to_the_Philosophy_of_Mathematics
Reasoning that is rationally compelling, though not deductively valid
logic is related mainly because, like paraconsistent logic, the reordering of premises can change the set of justified conclusions. Dialogue logics introduce
Defeasible_reasoning
(1929–2024), mathematician and logician, recognised for his works in paraconsistent logic Oswaldo Cruz (1872–1917), physician and public health champion, eliminated
List_of_Brazilian_scientists
Mathematical logician and philosopher
Bertrand Russell, Alfred North Whitehead, and David Hilbert were using logic and set theory to investigate the foundations of mathematics), building
Kurt_Gödel
Logical proposition that cannot be disproved
is metaphysically possible is also logically possible. Modal logic Paraconsistent logic Paradox Possibility theory Possible world Subjunctive possibility
Logical_possibility
inconsistency-tolerant (or paraconsistent) logic; furthermore, Jaśkowski was a pioneer in the investigation of both intuitionistic logic and free logic. Karol Borsuk
Timeline of Polish science and technology
Timeline_of_Polish_science_and_technology
Philosophical concept
logical constants), exist. Additionally, nontraditional logics, such as paraconsistent logics, allow contradictions to be possible, undermining Hale’s
Metaphysical_necessity
School of thought
Lwowsko-Warszawska) was an interdisciplinary school (mainly philosophy, logic and psychology) founded by Kazimierz Twardowski in 1895 in Lwów, Austro-Hungary
Lwów–Warsaw_school
Mathematician, philosopher, professor (born 1953)
Diderik; Priest, Graham; Mortensen, Chris (2000). Frontiers of paraconsistent logic. Baldock, Hertfordshire, England Philadelphia, Pennsylvania: Research
Jean_Paul_Van_Bendegem
Buddhist philosophy founded by Nagarjuna
regarded as a critic of logic (Inada 1970), as a defender of classical logic (Hayes 1994), and as a pioneer of paraconsistent logic (Garfield and Priest
Madhyamaka
Ancient French logician
Journal of Philosophy, 83, 1986, pp. 564 – 572. In particular p. 565 "Paraconsistent Logic (Stanford Encyclopedia of Philosophy)". Plato.stanford.edu. Retrieved
William_of_Soissons
Polish logician and philosopher (1878–1956)
Polish notation and Łukasiewicz logic. His work centred on philosophical logic, mathematical logic and history of logic. He thought innovatively about
Jan_Łukasiewicz
German philosopher, logician, and mathematician (1848–1925)
father of analytic philosophy, concentrating on the philosophy of language, logic, and mathematics. Though he was largely ignored during his lifetime, Giuseppe
Gottlob_Frege
American philosopher and logician (1940–2022)
and original contributions to logic, especially modal logic. His principal contribution is a semantics for modal logic involving possible worlds, now
Saul_Kripke
American philosopher (1941–2001)
philosophy of mind, philosophy of probability, epistemology, philosophical logic, aesthetics, philosophy of mathematics, philosophy of time, and philosophy
David_Lewis_(philosopher)
Polish–American mathematician (1901–1983)
metamathematics, and algebraic logic, he also contributed to abstract algebra, topology, geometry, measure theory, mathematical logic, set theory, type theory
Alfred_Tarski
American mathematician and computer scientist (1903–1995)
logician, and philosopher who made major contributions to mathematical logic and the foundations of theoretical computer science. He is best known for
Alonzo_Church
Canadian Expert in Climate Modelling
engineering, where he worked with Marsha Chechik on temporal and paraconsistent logics for proving properties of formal software specifications. He also
Steve_M._Easterbrook
Austrian philosopher and logician (1889–1951)
April 1889 – 29 April 1951) was an Austro-British philosopher who worked in logic, philosophy of mathematics, philosophy of mind, and philosophy of language
Ludwig_Wittgenstein
Property of predicates in linguistics and philosophy
Cobreros, (2011) "Paraconsistent Vagueness: A Positive Argument" Synthese 183(2): 211–227. Dominic Hyde and Mark Colyvan (2008) “Paraconsistent Vagueness: Why
Vagueness
American philosopher and logician (1908–2000)
1956 to 1978. Quine was a teacher of logic and set theory. He was famous for his position that first-order logic is the only kind worthy of the name,
Willard_Van_Orman_Quine
American philosopher (born 1941)
for his contributions to philosophy of science, epistemology and formal logic. He is a distinguished professor of philosophy at San Francisco State University
Bas_van_Fraassen
English philosopher (1910–1989)
promotion of logical positivism, particularly in his books Language, Truth, and Logic (1936) and The Problem of Knowledge (1956). Ayer was educated at Eton College
A._J._Ayer
PARACONSISTENT LOGIC
PARACONSISTENT LOGIC
Girl/Female
Hindu
Trick, Power, Strategy, Solution by logic, By reasoning
Girl/Female
Gujarati, Hindu, Indian, Kannada, Tamil
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
Tamil
Trick, Power, Strategy, Solution by logic, By reasoning
Boy/Male
Indian
Intelligent, Logical
Girl/Female
Arabic, Muslim, Pashtun
Logic; Reason
Girl/Female
Bengali, Hindu, Indian, Tamil, Telugu
Logically Intelligent; Who Stands Alone
Girl/Female
Hindu
Distinguished, Pure, Deep, Logically intelligent
Girl/Female
Indian
Successful; Logical Thinkers
Boy/Male
Hindu
Full of feathers, Full of logic, Name of sage, Vatsyayan
Girl/Female
Hindu
Distinguished, Pure, Deep, Logically intelligent
Girl/Female
Tamil
Trick, Power, Strategy, Solution by logic, By reasoning
Girl/Female
African, Arabic, French, Indian, Muslim, Swahili, Tamil
Intelligent; Logical; Intelligent One who Reasons; Wise
Boy/Male
Tamil
Full of feathers, Full of logic, Name of sage, Vatsyayan
Girl/Female
Tamil
Vivikta | விவிகதா
Distinguished, Pure, Deep, Logically intelligent
Vivikta | விவிகதா
Girl/Female
Danish, Hindu, Indian, Japanese
Ray of Light; Logical
Boy/Male
Hindu, Indian
Logical
Boy/Male
Hindu
Love and kindness, Analytical, Logical
Boy/Male
Tamil
Intelligent, Logical
PARACONSISTENT LOGIC
PARACONSISTENT LOGIC
Girl/Female
Australian, Danish, Finnish, French, German, Hawaiian, Hebrew, Scandinavian, Swedish
Noble Kind; God is My Oath; Similar to Elizabeth; Pledged to God; Consecrated to God; My God is a Vow
Boy/Male
Tamil
Sharvarish | à®·à®°à¯à®µà®°à®¿à®·
The Moon
Male
English
American English surname transferred to forename use, derived from Dutch de Raedt, from Middle Dutch raet, RHETT means "advice."
Boy/Male
Arabic, Pakistani
Minister
Boy/Male
Hindu
Lord  subramanya Swamy
Boy/Male
Tamil
Randheer | ரணதீர , ரணதீர
Light, Bright, Brave
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Given by Water; Cloud
Boy/Male
Welsh
Legendary Excalibur, King Arthur's sword.
Boy/Male
Muslim
Feel
Girl/Female
Tamil
PARACONSISTENT LOGIC
PARACONSISTENT LOGIC
PARACONSISTENT LOGIC
PARACONSISTENT LOGIC
PARACONSISTENT LOGIC
a.
Having or observing logical sequence; logically consistent and rigorous; consecutive in development or transition of thought.
a.
Half logical; partly logical; said of fallacies.
v. i.
Not possessing or manifesting intellectual, logical, moral, or political strength, vigor, etc.
n.
Of or pertaining to a place; limited; logical application; as, a topical remedy; a topical claim or privilege.
a.
According to the rules of logic; as, a logical argument or inference; the reasoning is logical.
a.
Skilled in logic; versed in the art of thinking and reasoning; as, he is a logical thinker.
a.
Not skillful; inexperienced; awkward; bungling; as, an unskillful surgeon or mechanic; an unskillful logician.
n.
A person skilled in logic.
n.
The art of reasoning; logic.
n.
Logicalness.
a.
Of or pertaining to logic; used in logic; as, logical subtilties.
n.
That which follows as the logical result of reasoning; inference; conclusion; suggestion.
adv.
In a logical manner; as, to argue logically.
a.
Consistent with one's self or with itself; not deviation from the ordinary standard by which the conduct is guided; logically consistent throughout; having each part consistent with the rest.
n.
A treatise on logic; as, Mill's Logic.
n.
The three " liberal" arts, grammar, logic, and rhetoric; -- being a triple way, as it were, to eloquence.
n.
See Logic.
n.
One of the seminaries for teaching logic, metaphysics, and theology, which were formed in the Middle Ages, and which were characterized by academical disputations and subtilties of reasoning.
n.
That quality which tends to secure results; effective power in an institution or enactment; security; validity; legal or moral force; logical conclusiveness; as, the strength of social or legal obligations; the strength of law; the strength of public opinion; strength of evidence; strength of argument.
n.
The quality of being logical.