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Propositional Logic: Semantics, Part 1
Propositional Logic: Semantics, Part 1
Published: 2015/06/04
Channel: David Agler
2.3 Semantics of Propositional Logic
2.3 Semantics of Propositional Logic
Published: 2012/10/12
Channel: Daniel Junior
What Makes a Sentence True or False? Predicate Logic
What Makes a Sentence True or False? Predicate Logic
Published: 2015/10/07
Channel: The Ling Space
What is meaning? Semantics, semiotics, logic & the meaning of words -- Linguistics & Logic 101
What is meaning? Semantics, semiotics, logic & the meaning of words -- Linguistics & Logic 101
Published: 2012/09/05
Channel: NativLang
SEM122 - Predicate Logic I
SEM122 - Predicate Logic I
Published: 2013/06/12
Channel: The Virtual Linguistics Campus
The semantics of predicate logic
The semantics of predicate logic
Published: 2015/04/14
Channel: G. Randolph Mayes
2 - 3 - 2.3 Semantics of Propositional Logic-Introduction to Logic-Professor Mike Genesereth
2 - 3 - 2.3 Semantics of Propositional Logic-Introduction to Logic-Professor Mike Genesereth
Published: 2012/05/02
Channel: OpenCourseOnline
Lecture 4: The semantics of propositional logic
Lecture 4: The semantics of propositional logic
Published: 2015/10/01
Channel: Logic for CS, Shai Ben-David, U Waterloo Fall 2015
Predicate Logic Semantics - Models
Predicate Logic Semantics - Models
Published: 2017/02/13
Channel: David Agler
Unit 7 - Module 1: Introduction to LTL
Unit 7 - Module 1: Introduction to LTL
Published: 2015/08/20
Channel: Model Checking
SEM121 - Entailment
SEM121 - Entailment
Published: 2013/05/16
Channel: The Virtual Linguistics Campus
semantics for propositional logic
semantics for propositional logic
Published: 2013/02/13
Channel: Wheeler Ruml
Philosophy 2020 (001): Basic Logic. Youtube Lecture 3 - Truth Functional Semantics
Philosophy 2020 (001): Basic Logic. Youtube Lecture 3 - Truth Functional Semantics
Published: 2011/10/25
Channel: Philosophy2020UWO
"Language and semantics of classical logic" - UNIT 1: CLASSICAL PROPOSITIONAL LOGIC
"Language and semantics of classical logic" - UNIT 1: CLASSICAL PROPOSITIONAL LOGIC
Published: 2017/01/27
Channel: Cursos On-Line Masivos
SEM121 - Propositions
SEM121 - Propositions
Published: 2013/05/08
Channel: The Virtual Linguistics Campus
SEM122 - Predicate Logic II
SEM122 - Predicate Logic II
Published: 2013/06/28
Channel: The Virtual Linguistics Campus
Vladimir Lifschitz "What answer set solvers tell us about the semantics of logic programs"
Vladimir Lifschitz "What answer set solvers tell us about the semantics of logic programs"
Published: 2012/11/21
Channel: Yegor Bryukhov
Unit 7 - Module 2: Semantics of LTL
Unit 7 - Module 2: Semantics of LTL
Published: 2015/08/20
Channel: Model Checking
Truth trees for propositional logic 1
Truth trees for propositional logic 1
Published: 2013/01/19
Channel: Kane B
Modal Logic (Basics)
Modal Logic (Basics)
Published: 2014/04/18
Channel: Carneades.org
The Semantics of Standard Deontic Logic
The Semantics of Standard Deontic Logic
Published: 2015/10/21
Channel: Carneades.org
Semantics of Reductionist Deontic Logic
Semantics of Reductionist Deontic Logic
Published: 2015/10/29
Channel: Carneades.org
Mod-01 Lec-19 Semantic Tableaux Method for Propositional Logic
Mod-01 Lec-19 Semantic Tableaux Method for Propositional Logic
Published: 2015/03/18
Channel: nptelhrd
Deep Natural Language Semantics - Raymond Mooney
Deep Natural Language Semantics - Raymond Mooney
Published: 2014/11/26
Channel: Allen Institute for Artificial Intelligence (AI2)
M2 Lec 1 - Propositional Logic: Language, Semantics and Reasoning
M2 Lec 1 - Propositional Logic: Language, Semantics and Reasoning
Published: 2016/01/12
Channel: NOC16 Jan-May CS02
Mod-04 Lec-03 Syntax and Semantics of CTL
Mod-04 Lec-03 Syntax and Semantics of CTL
Published: 2013/02/15
Channel: nptelhrd
Lecture: Unit 9 Predicate Logic Semantics Part I
Lecture: Unit 9 Predicate Logic Semantics Part I
Published: 2016/11/25
Channel: Alex Koo
Propositional Logic: Semantics, Part 2
Propositional Logic: Semantics, Part 2
Published: 2015/06/03
Channel: David Agler
[Mathematical Linguistics] Compositional Semantics with Predicate Logic
[Mathematical Linguistics] Compositional Semantics with Predicate Logic
Published: 2016/06/03
Channel: TheTrevTutor
Epistemic Logic: Kripke Semantics in a Multi Agent Scenario
Epistemic Logic: Kripke Semantics in a Multi Agent Scenario
Published: 2016/04/10
Channel: NOC16 Jan-May CS02
Modal Semantics & Metaphysics
Modal Semantics & Metaphysics
Published: 2013/05/19
Channel: Philosophical Overdose
[Mathematical Linguistics] Compositional Semantics with Propositional Logic
[Mathematical Linguistics] Compositional Semantics with Propositional Logic
Published: 2016/05/24
Channel: TheTrevTutor
Ontology, semantics and logic
Ontology, semantics and logic
Published: 2010/12/02
Channel: AProudAtheist
Mod-01 Lec-37 Semantics of Predicate Logic
Mod-01 Lec-37 Semantics of Predicate Logic
Published: 2015/03/18
Channel: nptelhrd
M3 Lec 2 - First Order Logic: Semantics
M3 Lec 2 - First Order Logic: Semantics
Published: 2016/01/12
Channel: NOC16 Jan-May CS02
Syntax vs Semantics (Philosophical Distinctions)
Syntax vs Semantics (Philosophical Distinctions)
Published: 2015/09/20
Channel: Carneades.org
Formal semantics (logic)
Formal semantics (logic)
Published: 2016/01/22
Channel: WikiAudio
Propositional Logic in Artificial Intelligence | PL | (Eng-Hindi) | #2
Propositional Logic in Artificial Intelligence | PL | (Eng-Hindi) | #2
Published: 2017/03/17
Channel: Well Academy
FOL (First Order Logic)
FOL (First Order Logic)
Published: 2015/07/20
Channel: Francisco Iacobelli
[Mathematical Linguistics] Compositional Semantics with Propositional Logic Examples
[Mathematical Linguistics] Compositional Semantics with Propositional Logic Examples
Published: 2016/05/26
Channel: TheTrevTutor
Semantics for Augmented Reductive Deontic Logic (KTd)
Semantics for Augmented Reductive Deontic Logic (KTd)
Published: 2015/10/30
Channel: Carneades.org
SEM120 - Sentence Semantics
SEM120 - Sentence Semantics
Published: 2013/04/05
Channel: The Virtual Linguistics Campus
Modal logic 1.1 - system K - introduction
Modal logic 1.1 - system K - introduction
Published: 2013/01/23
Channel: Kane B
ICTAC2015 Conference - Oral Session on Logic and Semantics
ICTAC2015 Conference - Oral Session on Logic and Semantics
Published: 2015/12/10
Channel: ICTAC2015
1-3 Discrete Mathematics - Propositional Logic - The Semantics of Propositional Logic
1-3 Discrete Mathematics - Propositional Logic - The Semantics of Propositional Logic
Published: 2015/10/13
Channel: yoitsfrancis
Oracle Semantics for Concurrent Separation Logic
Oracle Semantics for Concurrent Separation Logic
Published: 2016/09/08
Channel: Microsoft Research
What does formal semantics mean?
What does formal semantics mean?
Published: 2015/03/29
Channel: What Does That Mean?
5 - 3 - 6.3 Semantics-Introduction to Logic-Professor Mike Genesereth
5 - 3 - 6.3 Semantics-Introduction to Logic-Professor Mike Genesereth
Published: 2012/05/20
Channel: OpenCourseOnline
Brandom on Incompatibility, Modal Semantics & Intrinsic Logic (with Jaroslav Peregrin)
Brandom on Incompatibility, Modal Semantics & Intrinsic Logic (with Jaroslav Peregrin)
Published: 2013/05/14
Channel: Philosophical Overdose
Predicate Logic Symbolization Summary
Predicate Logic Symbolization Summary
Published: 2007/04/17
Channel: jellologic
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WIKIPEDIA ARTICLE

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In logic, the semantics of logic is the study of the semantics, or interpretations, of formal and (idealizations of) natural languages usually trying to capture the pre-theoretic notion of entailment.

Overview[edit]

The truth conditions of various sentences we may encounter in arguments will depend upon their meaning, and so logicians cannot completely avoid the need to provide some treatment of the meaning of these sentences. The semantics of logic refers to the approaches that logicians have introduced to understand and determine that part of meaning in which they are interested; the logician traditionally is not interested in the sentence as uttered but in the proposition, an idealised sentence suitable for logical manipulation.[citation needed]

Until the advent of modern logic, Aristotle's Organon, especially De Interpretatione, provided the basis for understanding the significance of logic. The introduction of quantification, needed to solve the problem of multiple generality, rendered impossible the kind of subject-predicate analysis that governed Aristotle's account, although there is a renewed interest in term logic, attempting to find calculi in the spirit of Aristotle's syllogistic but with the generality of modern logics based on the quantifier.

The main modern approaches to semantics for formal languages are the following:

  • Model-theoretic semantics is the archetype of Alfred Tarski's semantic theory of truth, based on his T-schema, and is one of the founding concepts of model theory. This is the most widespread approach, and is based on the idea that the meaning of the various parts of the propositions are given by the possible ways we can give a recursively specified group of interpretation functions from them to some predefined mathematical domains: an interpretation of first-order predicate logic is given by a mapping from terms to a universe of individuals, and a mapping from propositions to the truth values "true" and "false". Model-theoretic semantics provides the foundations for an approach to the theory of meaning known as Truth-conditional semantics, which was pioneered by Donald Davidson. Kripke semantics introduces innovations, but is broadly in the Tarskian mold.
  • Proof-theoretic semantics associates the meaning of propositions with the roles that they can play in inferences. Gerhard Gentzen, Dag Prawitz and Michael Dummett are generally seen as the founders of this approach; it is heavily influenced by Ludwig Wittgenstein's later philosophy, especially his aphorism "meaning is use".
  • Truth-value semantics (also commonly referred to as substitutional quantification) was advocated by Ruth Barcan Marcus for modal logics in the early 1960s and later championed by Dunn, Belnap, and Leblanc for standard first-order logic. James Garson has given some results in the areas of adequacy for intensional logics outfitted with such a semantics. The truth conditions for quantified formulas are given purely in terms of truth with no appeal to domains whatsoever (and hence its name truth-value semantics).
  • Game-theoretical semantics has made a resurgence lately mainly due to Jaakko Hintikka for logics of (finite) partially ordered quantification which were originally investigated by Leon Henkin, who studied Henkin quantifiers.
  • Probabilistic semantics originated from H. Field and has been shown equivalent to and a natural generalization of truth-value semantics. Like truth-value semantics, it is also non-referential in nature.

See also[edit]

References[edit]

  • Jaakko Hintikka (2007), Socratic Epistemology: Explorations of Knowledge-Seeking by Questioning, Cambridge: Cambridge University Press.
  • Ilkka Niiniluoto (1999), Critical Scientific Realism, Oxford: Oxford University Press.

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