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Longer titles found: Non-classical logic (view), Journal of Applied Non-Classical Logics (view), An Introduction to Non-Classical Logic (view)

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alternate case: classical logic

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The Temperature paradox or Partee's paradox is a classic puzzle in formal semantics and philosophical logic. Formulated by Barbara Partee in the 1970s

Alternative semantics (or Hamblin semantics) is a framework in formal semantics and logic. In alternative semantics, expressions denote alternative sets

Intensional logic is an approach to predicate logic that extends first-order logic, which has quantifiers that range over the individuals of a universe

The World of Null-A, sometimes written The World of Ā, is a 1948 science fiction novel by Canadian-American writer A. E. van Vogt. It was originally published

Probabilistic logic (also probability logic and probabilistic reasoning) involves the use of probability and logic to deal with uncertain situations. Probabilistic

these computational basis states. Quantum logic gates, in contrast to classical logic gates, are always reversible. One requires a special kind of reversible

An infinitary logic is a logic that allows infinitely long statements and/or infinitely long proofs. The concept was introduced by Zermelo in the 1930s

A probabilistic logic network (PLN) is a conceptual, mathematical and computational approach to uncertain inference. It was inspired by logic programming

blocks of quantum circuits, like classical logic gates are for conventional digital circuits. Unlike many classical logic gates, quantum logic gates are

Noneism, also known in philosophy as modal Meinongianism (named after Alexius Meinong), names both a philosophical theory and an unrelated religious trend

Defeasible logic is a non-monotonic logic proposed by Donald Nute to formalize defeasible reasoning. In defeasible logic, there are three different types

In mathematics and computer science, a canonical, normal, or standard form of a mathematical object is a standard way of presenting that object as a mathematical

logic as the logic of quantum information theory (in exact analogy to classical logic being founded on Cartesian closed categories). Suppose that there are

Default logic is a non-monotonic logic proposed by Raymond Reiter to formalize reasoning with default assumptions. Default logic can express facts like

Subjective logic is a type of probabilistic logic that explicitly takes epistemic uncertainty and source trust into account. In general, subjective logic

Preferential entailment is a non-monotonic logic based on selecting only models that are considered the most plausible. The plausibility of models is expressed

also introduced the construct of 'abduction' as an alternative to classical logic (deduction and induction). The 'use-centered' approach assumes abduction

In mathematics, an R-function, or Rvachev function, is a real-valued function whose sign does not change if none of the signs of its arguments change;

verification of theorems, and other deductions in classical and non-classical logic. The journal is published by Springer Science+Business Media. As of

verification of theorems, and other deductions in classical and non-classical logic. The journal is published by Springer Science+Business Media. As of

negation of any statement is equivalent to the original statement in classical logic, the inverse of the inverse is logically equivalent to the original

In proof theory, the Dialectica interpretation is a proof interpretation of intuitionistic logic (Heyting arithmetic) into a finite type extension of primitive

In logic, inference is the process of deriving logical conclusions from premises known or assumed to be true. In checking a logical inference for formal

The modal fallacy or modal scope fallacy is a type of formal fallacy that occurs in modal logic. It is the fallacy of placing a proposition in the wrong

time to be usable by quantum logic gates (cf. propagation delay for classical logic gates). Since the development of the first quantum computer in 1998

Linguistic Society of America. Horn's primary research program lies in classical logic, lexical semantics, and neo-Gricean pragmatic theory. He mainly focused

formalization of dialectics also attracted scholars by applying formal non-classical logic such as paraconsistent logic. Wald, Henri (January 1975). Introduction

In logic, a rational consequence relation is a non-monotonic consequence relation satisfying certain properties listed below. A rational consequence relation

Circumscription is a non-monotonic logic created by John McCarthy to formalize the common sense assumption that things are as expected unless otherwise

In nonmonotonic reasoning, the Nixon diamond is a scenario in which default assumptions lead to mutually inconsistent conclusions. The scenario is: usually

Graham. Introduction to Non-Classical Logic, Cambridge University Press, 2001. 2nd edition: Introduction to Non-Classical Logic: From If to Is, Cambridge

editors, Handbook of Philosophical Logic, volume II: Extensions of Classical Logic, chapter 10, pages 497-604. Reidel, Dordrecht, 1984. David Harel, Dexter

already over minimal logic. This also means that Piece's law entails classical logic over intuitionistic logic. This is shown below. Firstly, from P → Q

Logic is an emerging interdisciplinary field involving logic, non-classical logic, categorical logic, set theory, foundation of logic, and the philosophy

..] For these, even for such theorems as were deduced by means of classical logic, they postulated an existence and exactness independent of language

Plausible reasoning is a method of deriving new conclusions from given known premises, a method different from the classical syllogistic argumentation

and K. Gödel on embedding operations that transform a formula F of classical logic into a formula Fᶜ' of intuitionistic (constructive) logic, such that

empty domain is the empty set having no members. In traditional and classical logic domains are restrictedly non-empty in order that certain theorems be

Fine", (back matter from Kit Fine on Truthmakers, Relevance, and Non-classical Logic). Semantic relationism is the thesis that the content of utterances

∀ quantifiers in classical logic. These are dual because ∃x.¬P(x) and ¬∀x.P(x) are equivalent for all predicates P in classical logic: if there exists

obvious intertranslation between IF formulas and formulas of some classical logic system. However, there is a translation procedure of IF formulas into

3. N 1, pp. 48–56 Bazhanov, V.A. The Origins and Emergence of Non-Classical Logic in Russia (Nineteenth Century until the Turn of the Twentieth Century)

from the underlying principles of quantum mechanics, that the laws of classical logic, classical probability and classical dynamics apply to objects at the

the application of George Spencer-Brown’s work to the practice of classical logic, and the analysis of story structure. Conrad's designs have been published

analysis, which is built upon a foundation of constructive, rather than classical, logic and set theory. Intuitionistic analysis, which is developed from constructive

In formal semantics, Strawson entailment is a variant of the concept of entailment which is insensitive to presupposition failures. Formally, a sentence

Birkhoff and John von Neumann, abandons the law of distributivity from classical logic in order to reconcile some of the apparent inconsistencies of classical

(x\leq y\lor y\leq x)} , the double-negated strong connectedness. In a classical logic context, " ≤ {\displaystyle \leq } " thus constitutes a (non-strict)

collection in the Russell paradox, cannot be a set in any set theory with classical logic. But the collection of order types in New Foundations (defined as equivalence

Logically self-contradictory statement Relevance logic – A kind of non-classical logic Scientific misconceptions – False beliefs about science Sophist – Teachers

experiments – but we can now be mathematically exact about the limits of classical logic. HPO formalism Hohenberg, P. C. (2010-10-05). "Colloquium : An introduction

the real number's linearly ordered group structure for addition. In classical logic, this axiom of trichotomy holds for ordinary comparisons between real

control is passed explicitly Kripke semantics – Formal semantics for non-classical logic systems Situation semantics – Concept in situation theory Temperature

reasoning Imprecise probability C. J. van Rijsbergen (1986), A non-classical logic for information retrieval (PDF), The Computer Journal, pp. 481–485

theory of inquiry was extracted by Peirce from its raw materials in classical logic, with a little bit of help from Kant, and refined in parallel with

systems of symbolic logic Kripke semantics – Formal semantics for non-classical logic systems Relevance theory – Theory of cognitive linguistics Salience

P". Similarly, intuitionists object to the existence property for classical logic, where one can prove ∃ x . ϕ ( x ) {\displaystyle \exists x.\phi (x)}

constructive analysis). The theorem is a foregone conclusion over classical logic, where law of the excluded middle is assumed. The proof below is therefore

\lnot B)\\(\lnot A&\lor \lnot B)\\(\lnot A&\land C)\end{aligned}}} In classical logic and many modal logics, every formula can be brought into this form

theory of truth that combines an unrestricted truth predicate with classical logic. Revision theory takes truth to be a circular concept, defined by the

supports so-called explicit negation, which is closer to negation in classical logic. Flora-2 is an extension of F-logic with HiLog, transaction logic,

Frege to Gödel: A Source Book on Mathematical Logic. Harvard Univ. Press. Stanford Encyclopedia of Philosophy: "Classical Logic—by Stewart Shapiro. v t e

system of Polish notation that names all 16 binary connectives of classical logic which is a compatible extension of the notation of Łukasiewicz in 1929

intuitionistic logic) Peirce's law (((P→Q)→P)→P) is a theorem. For classical logic, it can be easily verified with a truth table. The study of mathematical

of knowledge. Indian logic was influenced by grammar, and Greek (or classical) logic was influenced by mathematics. Vidyabhusana (1921), Randle (1930) and

flaws and of great beauty and wide applicability, and attacks against classical logic are largely unjustified. Freytag-Löringhoff was a staunch proponent

that, while coherent and valid, differ from some theorems grounded in classical logic. Formalism denies logical or intuitive meanings altogether, making

detailed argumentation, attention to semantics, use of classical logic and non-classical logic and clarity of meaning above all other criteria. Though

Vampire (theorem prover), an automated theorem prover for first-order classical logic RPG-29 "Vampir", a Russian rocket-propelled grenade launcher El Vampiro

mathematical description of reality. We can now demonstrate that the laws of classical logic, classical probability, and classical dynamics (of common sense, in

Illinois. 1965, Cybernetics and the Transition from Classical to Trans-Classical Logic. Illinois University Biological Computer Laboratory BCL Report 3.0

principles of logic', challenged the belief that the rules of the classical logic, which have come down to us essentially from Aristotle (384--322 B

the Dutch logician Evert Willem Beth (Beth 1955) and simplified, for classical logic, by Raymond Smullyan (Smullyan 1968, 1995). Smullyan's simplification

classical reversible computation, as both CNOT and Toffoli are also classical logic gates. Since the quantum Fourier transform has a low circuit complexity

conclusion on the assumptions. Another definition of normal derivation in classical logic is: A derivation in NK is normal if all major premisses of E-rules

as logic programming has an appealing neural implementation, unlike classical logic." In The Proper Treatment of Events, Michiel van Lambalgen and Fritz

The God Who Loves You (2004) Socratic Logic (2005) — A textbook on classical logic You Can Understand the Bible (2005) — a combination of his previous

{\displaystyle Q_{n}} is obtained by measuring several qubits and apply some (classical) logic gates to them. We can always defer the measurement and reroute the

realizability was introduced by Krivine and extends realizability to classical logic. It furthermore realizes axioms of Zermelo–Fraenkel set theory. Understood

quantification on infinite sets, and this cannot be formalized in the classical logic of first-order predicates. This is one of the reasons for which higher-order

proving any truth Pluralist theories of truth Principle of bivalence – Classical logic of two values, either true or false Propositional logic – System of

Association for Automated Reasoning Fully automated theorem provers for classical logic United States World Computer-Bridge Championship American Contract

false") and other semantic paradoxes that requires a modification of classical logic. In The Metaphysics Within Physics (2007) the central idea is that

( i ) := τ ( Π ( i ) ) {\displaystyle \mu C(i):=\tau (\Pi (i))} In classical logic the truth values are certain. Therefore a classification is crisp,

(A\to \Box A)\to A)\to A} over K. The smallest modal companion of classical logic (CPC) is Lewis' S5, whereas its largest modal companion is the logic

logic gates, analogous to how classical memory can be manipulated with classical logic gates. One important gate for both classical and quantum computation

nonstandard analysis. In terms of conventional mathematical foundations in classical logic, such results are quite acceptable although usually strongly dependent

(B\land A)} . It was also demonstrated that the laws of distribution of classical logic, P ∨ ( Q ∧ R ) = {\displaystyle P\lor (Q\land R)={}} ( P ∨ Q ) ∧ (

founded a new logic, questioning the tertium non datur principle of classical logic. He introduced a third state, going beyond the duality principle, the

domain. However, whenever instantaneous logic must be interfaced with classical logic schemes, the interface must use correlator-based logic gates for an

meaning postulate or axiom): if p then q (equivalent to q or not-p in classical logic, not necessarily in other logics) Defeasible (from authority): if p

analysis have roots in category theory. This approach departs from the classical logic used in conventional mathematics by denying the general applicability

organized into a lattice, in which the distributive law, valid in classical logic, is weakened, to reflect the fact that in quantum physics, not all

15 February 2022. Shapiro, Stewart; Kouri Kissel, Teresa (2022). "Classical Logic". The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab

ISBN 978-0-19-988268-7. Shapiro, Stewart; Kouri Kissel, Teresa (2022). "Classical Logic". The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab

Characteristics of the Referential and Inferential Predication in Classical Logic in The Logical Foresight, 1/2021. New Remarks on the Concept in Logical

One motivation of this position is to avoid certain paradoxes in classical logic and set theory, like the liar's paradox and Russell's paradox. One

in fuzzy logic connects a symbol that is typically a predicate in classical logic (e.g., "John is Bold", or in predicate logic – Bold(John)) – to linguistic

This differentiates Llull's system from Aristotelian logic; because classical logic did not take the powers of the soul into account, it was—thereby, in

19 September 2024. Shapiro, Stewart; Kouri Kissel, Teresa (2024). "Classical Logic". The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab

an Interactive Lawyer (see here) Denecker, Marc (2000). "Extending classical logic with inductive definitions". International Conference on Computational