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What is PROOF-THEORETIC SEMANTICS? What does PROOF-THEORETIC SEMANTICS mean
What is PROOF-THEORETIC SEMANTICS? What does PROOF-THEORETIC SEMANTICS mean
Published: 2017/04/29
Channel: The Audiopedia
Heinrich Wansing - Compositionality in Proof-Theoretic Semantics [pt.1] (2015)
Heinrich Wansing - Compositionality in Proof-Theoretic Semantics [pt.1] (2015)
Published: 2015/09/27
Channel: Logic UFRN
Heinrich Wansing - Compositionality in Proof-Theoretic Semantics [pt.2] (2015)
Heinrich Wansing - Compositionality in Proof-Theoretic Semantics [pt.2] (2015)
Published: 2015/09/27
Channel: Logic UFRN
1.4 Proof theoretic validity
1.4 Proof theoretic validity
Published: 2013/06/13
Channel: Chico Jones
What is COHERENTISM? What does COHERENTISM mean? COHERENTISM meaning, definition & explanation
What is COHERENTISM? What does COHERENTISM mean? COHERENTISM meaning, definition & explanation
Published: 2016/06/16
Channel: The Audiopedia
What is INFERENTIAL ROLE SEMANTICS? What does INFERENTIAL ROLE SEMANTICS mean?
What is INFERENTIAL ROLE SEMANTICS? What does INFERENTIAL ROLE SEMANTICS mean?
Published: 2017/04/15
Channel: The Audiopedia
Theories, Solvers and Static Analysis by Abstract Interpretation
Theories, Solvers and Static Analysis by Abstract Interpretation
Published: 2016/08/17
Channel: Microsoft Research
2.4 K  proof theoretic validity
2.4 K proof theoretic validity
Published: 2013/06/24
Channel: Chico Jones
Mod-01 Lec-18 The Semantic of Predicate Logic
Mod-01 Lec-18 The Semantic of Predicate Logic
Published: 2012/09/03
Channel: nptelhrd
What is TRUTH-CONDITIONAL SEMANTICS? What does TRUTH-CONDITIONAL SEMANTICS mean?
What is TRUTH-CONDITIONAL SEMANTICS? What does TRUTH-CONDITIONAL SEMANTICS mean?
Published: 2017/04/27
Channel: The Audiopedia
What are the limits of mathematical explanation? An interview with David Charles McCarty
What are the limits of mathematical explanation? An interview with David Charles McCarty
Published: 2015/01/26
Channel: Copernicus Center for Interdisciplinary Studies
"Logical consequence" - UNIT 1: CLASSICAL PROPOSITIONAL LOGIC
"Logical consequence" - UNIT 1: CLASSICAL PROPOSITIONAL LOGIC
Published: 2017/01/27
Channel: Cursos On-Line Masivos
Understanding & Inference
Understanding & Inference
Published: 2013/12/19
Channel: Philosophical Overdose
LambdaConf 2015 - Type Theory and its Meaning Explanations   Jon Sterling
LambdaConf 2015 - Type Theory and its Meaning Explanations Jon Sterling
Published: 2016/01/04
Channel: Confreaks
Modal logic 1.5 - logical consequence in K
Modal logic 1.5 - logical consequence in K
Published: 2013/02/07
Channel: Kane B
What is NON-MONOTONIC LOGIC? What does NON-MONOTONIC LOGIC mean? NON-MONOTONIC LOGIC meaning
What is NON-MONOTONIC LOGIC? What does NON-MONOTONIC LOGIC mean? NON-MONOTONIC LOGIC meaning
Published: 2017/01/25
Channel: The Audiopedia
The
The 'Fitting Problem' for Logical Semantic Systems
Published: 2013/10/05
Channel: Philosophical Overdose
What is CATEGORICAL LOGIC? What does CATEGORICAL LOGIC mean? CATEGORICAL LOGIC meaning & explanation
What is CATEGORICAL LOGIC? What does CATEGORICAL LOGIC mean? CATEGORICAL LOGIC meaning & explanation
Published: 2016/10/07
Channel: The Audiopedia
M. Sadrzadeh: "A generalised quantifier theory of natural language in categorical semantics"
M. Sadrzadeh: "A generalised quantifier theory of natural language in categorical semantics"
Published: 2016/06/30
Channel: OxfordQuantumVideo
Mod-01 Lec-23 Predicate Logic: Proof Theory (Contd..)
Mod-01 Lec-23 Predicate Logic: Proof Theory (Contd..)
Published: 2012/09/03
Channel: nptelhrd
What is CIRQUENT CALCULUS? What does CIRQUENT CALCULUS mean? CIRQUENT CALCULUS meaning & explanation
What is CIRQUENT CALCULUS? What does CIRQUENT CALCULUS mean? CIRQUENT CALCULUS meaning & explanation
Published: 2017/10/26
Channel: The Audiopedia
Proof by Construction
Proof by Construction
Published: 2015/07/20
Channel: FREGE: A Logic Course Elaine Rich, Alan Cline
cse471 s12 week7 1
cse471 s12 week7 1
Published: 2012/03/08
Channel: Subbarao Kambhampati
A CLP Approach to Modelling Systems
A CLP Approach to Modelling Systems
Published: 2016/09/06
Channel: Microsoft Research
Models as Structures: The Structural Semantics of Model-based design
Models as Structures: The Structural Semantics of Model-based design
Published: 2016/09/07
Channel: Microsoft Research
Logic & Language - quantifiers & bound variables (Logic 3 of 5)
Logic & Language - quantifiers & bound variables (Logic 3 of 5)
Published: 2011/09/02
Channel: NativLang
Godel
Godel's Incompleteness Theorem (Doubting Math)
Published: 2014/02/19
Channel: Carneades.org
Constructive knowledge
Constructive knowledge
Published: 2015/10/11
Channel: myetex
Tarski
Tarski's semantic theory of truth
Published: 2012/03/27
Channel: Frege100
Compositional semantics and event semantics
Compositional semantics and event semantics
Published: 2014/11/25
Channel: Lucas Champollion
1.3 Semantic validity
1.3 Semantic validity
Published: 2013/06/13
Channel: Chico Jones
KnowULinguistics - Compositionality (1)
KnowULinguistics - Compositionality (1)
Published: 2012/09/06
Channel: castview
Compositionally, Adequacy, and Full Abstraction
Compositionally, Adequacy, and Full Abstraction
Published: 2016/12/05
Channel: Simons Institute
What is COMPUTABILITY LOGIC? What does COMPUTABILITY LOGIC mean? COMPUTABILITY LOGIC meaning
What is COMPUTABILITY LOGIC? What does COMPUTABILITY LOGIC mean? COMPUTABILITY LOGIC meaning
Published: 2017/02/20
Channel: The Audiopedia
Loop invariants
Loop invariants
Published: 2013/05/11
Channel: Verification Corner
What Are The Basic Principles Of Logic?
What Are The Basic Principles Of Logic?
Published: 2017/11/09
Channel: Laimbo Lasu
Propositional Logic Proofs: Two Types of Derivation Rules (Intelim)
Propositional Logic Proofs: Two Types of Derivation Rules (Intelim)
Published: 2016/06/26
Channel: David Agler
Understanding Short Texts through Semantic Enrichment and Hashing
Understanding Short Texts through Semantic Enrichment and Hashing
Published: 2016/09/14
Channel: 1 Crore Projects Vadapalani
Frege
Frege's Puzzle (Philosophy of Language)
Published: 2015/03/16
Channel: Carneades.org
Protocol Composition Logics
Protocol Composition Logics
Published: 2016/09/06
Channel: Microsoft Research
Long Term Memory | Tulving (1972) | Procedural, Semantic & Episodic
Long Term Memory | Tulving (1972) | Procedural, Semantic & Episodic
Published: 2017/02/02
Channel: Psychology Unlocked
Wilfried Sieg  : The concept of computation: an axiomatic characterization
Wilfried Sieg : The concept of computation: an axiomatic characterization
Published: 2015/06/30
Channel: IHPST
5 - Kick-off afternoon : Vladimir Voevodsky, Univalent Foundations
5 - Kick-off afternoon : Vladimir Voevodsky, Univalent Foundations
Published: 2014/04/23
Channel: Institut Henri Poincaré
What is SEQUENT CALCULUS? What does SEQUENT CALCULUS mean? SEQUENT CALCULUS meaning & explanation
What is SEQUENT CALCULUS? What does SEQUENT CALCULUS mean? SEQUENT CALCULUS meaning & explanation
Published: 2017/10/26
Channel: The Audiopedia
1.4.4 practice
1.4.4 practice
Published: 2013/06/13
Channel: Chico Jones
Andrew Critch – Logical Induction – EAG 2016
Andrew Critch – Logical Induction – EAG 2016
Published: 2016/09/13
Channel: Machine Intelligence Research Institute
1.1 Logic and the propositional calculus
1.1 Logic and the propositional calculus
Published: 2013/06/12
Channel: Chico Jones
What is a Gödel Number? (Arithmatization)
What is a Gödel Number? (Arithmatization)
Published: 2016/03/27
Channel: Carneades.org
2.1 Modal logic and K
2.1 Modal logic and K
Published: 2013/06/23
Channel: Chico Jones
And Logic Begat Computer Science: When Giants Roamed the Earth
And Logic Begat Computer Science: When Giants Roamed the Earth
Published: 2014/04/24
Channel: Eric Smalls
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WIKIPEDIA ARTICLE

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Proof-theoretic semantics is an approach to the semantics of logic that attempts to locate the meaning of propositions and logical connectives not in terms of interpretations, as in Tarskian approaches to semantics, but in the role that the proposition or logical connective plays within the system of inference.

Gerhard Gentzen is the founder of proof-theoretic semantics, providing the formal basis for it in his account of cut-elimination for the sequent calculus, and some provocative philosophical remarks about locating the meaning of logical connectives in their introduction rules within natural deduction. The history of proof-theoretic semantics since then has been devoted to exploring the consequences of these ideas.[citation needed]

Dag Prawitz extended Gentzen's notion of analytic proof to natural deduction, and suggested that the value of a proof in natural deduction may be understood as its normal form. This idea lies at the basis of the Curry–Howard isomorphism, and of intuitionistic type theory. His inversion principle lies at the heart of most modern accounts of proof-theoretic semantics.

Michael Dummett introduced the very fundamental idea of logical harmony, building on a suggestion of Nuel Belnap. In brief, a language, which is understood to be associated with certain patterns of inference, has logical harmony if it is always possible to recover analytic proofs from arbitrary demonstrations, as can be shown for the sequent calculus by means of cut-elimination theorems and for natural deduction by means of normalisation theorems. A language that lacks logical harmony will suffer from the existence of incoherent forms of inference: it will likely be inconsistent.

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