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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.2] (2015)
Heinrich Wansing - Compositionality in Proof-Theoretic Semantics [pt.2] (2015)
Published: 2015/09/27
Channel: Logic UFRN
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
Theories, Solvers and Static Analysis by Abstract Interpretation
Theories, Solvers and Static Analysis by Abstract Interpretation
Published: 2016/08/17
Channel: Microsoft Research
Arno Bastenhof: "Phase semantics and focused proof search for the Lambek-Grishin calculus"
Arno Bastenhof: "Phase semantics and focused proof search for the Lambek-Grishin calculus"
Published: 2012/05/01
Channel: OxfordQuantumVideo
Loop invariants
Loop invariants
Published: 2013/05/11
Channel: Verification Corner
2.4 K  proof theoretic validity
2.4 K proof theoretic validity
Published: 2013/06/24
Channel: Chico Jones
Volker Halbach :  Representing self reference in arithmetic
Volker Halbach : Representing self reference in arithmetic
Published: 2015/06/30
Channel: IHPST
1.4 Proof theoretic validity
1.4 Proof theoretic validity
Published: 2013/06/13
Channel: Chico Jones
Long Term Memory | Tulving (1972) | Procedural, Semantic & Episodic
Long Term Memory | Tulving (1972) | Procedural, Semantic & Episodic
Published: 2017/02/02
Channel: Psychology Unlocked
Modal logic 1.5 - logical consequence in K
Modal logic 1.5 - logical consequence in K
Published: 2013/02/07
Channel: Kane B
Model Theory - part 07 - Semantics pt 1
Model Theory - part 07 - Semantics pt 1
Published: 2016/03/04
Channel: Taylor Dupuy's Math Vlog
Understanding & Inference
Understanding & Inference
Published: 2013/12/19
Channel: Philosophical Overdose
Compositional semantics and event semantics
Compositional semantics and event semantics
Published: 2014/11/25
Channel: Lucas Champollion
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
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
Tarski
Tarski's semantic theory of truth
Published: 2012/03/27
Channel: Frege100
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
Sanjeev Arora on "A theoretical approach to semantic representations"
Sanjeev Arora on "A theoretical approach to semantic representations"
Published: 2016/11/30
Channel: CMU Theory
CLE4Science Colloquia: Stephen Read
CLE4Science Colloquia: Stephen Read
Published: 2015/02/05
Channel: Fabio Bertato
Compositionally, Adequacy, and Full Abstraction
Compositionally, Adequacy, and Full Abstraction
Published: 2016/12/05
Channel: Simons Institute
How Complex is Natural Language? The Chomsky Hierarchy
How Complex is Natural Language? The Chomsky Hierarchy
Published: 2016/03/02
Channel: The Ling Space
What is a Gödel Number? (Arithmatization)
What is a Gödel Number? (Arithmatization)
Published: 2016/03/27
Channel: Carneades.org
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
Catarina Dutilh Novaes : Mathematical proofs: between orality and writing
Catarina Dutilh Novaes : Mathematical proofs: between orality and writing
Published: 2015/09/03
Channel: IHPST
Natural Logic and Alignment in Natural Language Inference
Natural Logic and Alignment in Natural Language Inference
Published: 2016/09/06
Channel: Microsoft Research
Jean Pierre Marquis : Axiomatization as conceptual design
Jean Pierre Marquis : Axiomatization as conceptual design
Published: 2015/09/03
Channel: IHPST
"Logical consequence" - UNIT 1: CLASSICAL PROPOSITIONAL LOGIC
"Logical consequence" - UNIT 1: CLASSICAL PROPOSITIONAL LOGIC
Published: 2017/01/27
Channel: Cursos On-Line Masivos
Constructive knowledge
Constructive knowledge
Published: 2015/10/11
Channel: myetex
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
cse471 s12 week7 1
cse471 s12 week7 1
Published: 2012/03/08
Channel: Subbarao Kambhampati
The
The 'Fitting Problem' for Logical Semantic Systems
Published: 2013/10/05
Channel: Philosophical Overdose
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
Being, Univocity, & Logical Syntax
Being, Univocity, & Logical Syntax
Published: 2017/07/18
Channel: Philosophical Overdose
Modern Physics Formalized in Modal Homotopy Type Theory by Urs Schreiber
Modern Physics Formalized in Modal Homotopy Type Theory by Urs Schreiber
Published: 2017/07/12
Channel: FOMUS 2016
Microbiome Discovery 19: Compositionality
Microbiome Discovery 19: Compositionality
Published: 2016/04/01
Channel: Dan Knights
Logic & Language - quantifiers & bound variables (Logic 3 of 5)
Logic & Language - quantifiers & bound variables (Logic 3 of 5)
Published: 2011/09/02
Channel: NativLang
Counterpart Theory and Quantified Modal Logic (Lewis)
Counterpart Theory and Quantified Modal Logic (Lewis)
Published: 2014/02/21
Channel: BlueSpectacles
KnowULinguistics - Compositionality (1)
KnowULinguistics - Compositionality (1)
Published: 2012/09/06
Channel: castview
1.3 Semantic validity
1.3 Semantic validity
Published: 2013/06/13
Channel: Chico Jones
10 Carnap and McKinsey: Topics in the Pre-history of Possible-worlds semantics by Max Cresswell
10 Carnap and McKinsey: Topics in the Pre-history of Possible-worlds semantics by Max Cresswell
Published: 2013/02/28
Channel: matsciencechannel
What is COMBINATORY LOGIC? What does COMBINATORY LOGIC mean? COMBINATORY LOGIC meaning
What is COMBINATORY LOGIC? What does COMBINATORY LOGIC mean? COMBINATORY LOGIC meaning
Published: 2017/02/14
Channel: The Audiopedia
Ivan Mikirtumov. Compositionality and Non-Compositionality: An Approach from Pragmatics
Ivan Mikirtumov. Compositionality and Non-Compositionality: An Approach from Pragmatics
Published: 2015/10/27
Channel: Виктор Горбатов
1 07  Sequent Calculus as a Compiler Intermediate Language
1 07 Sequent Calculus as a Compiler Intermediate Language
Published: 2016/10/02
Channel: ICFP Video
DeyPoS: Deduplicatable Dynamic Proof of Storage for Multi-User Environments
DeyPoS: Deduplicatable Dynamic Proof of Storage for Multi-User Environments
Published: 2016/11/15
Channel: jpinfotechprojects
Model Theory - part 08 - Semantics pt 2
Model Theory - part 08 - Semantics pt 2
Published: 2016/03/04
Channel: Taylor Dupuy's Math Vlog
Propositional Satisfiability
Propositional Satisfiability
Published: 2016/08/27
Channel: Professor Heather Pierce
KnowULinguistics - Compositionality (2)
KnowULinguistics - Compositionality (2)
Published: 2012/09/05
Channel: castview
Logic and Knowledge - D. Prawitz - J. Murzi - Conference - Rome - June 2011
Logic and Knowledge - D. Prawitz - J. Murzi - Conference - Rome - June 2011
Published: 2013/03/23
Channel: Logic & Knowledge
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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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References[edit]

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