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Propositional Logic: Syntax, Part 1
Propositional Logic: Syntax, Part 1
Published: 2015/05/28
Channel: David Agler
Predicate Logic: Basic Syntax
Predicate Logic: Basic Syntax
Published: 2017/02/07
Channel: David Agler
syntax and logic errors : definitions and causes
syntax and logic errors : definitions and causes
Published: 2015/09/17
Channel: Lord Logic's Computer Science channel
Mod-01 Lec-02 Propositional Logic Syntax
Mod-01 Lec-02 Propositional Logic Syntax
Published: 2012/09/03
Channel: nptelhrd
Syntax vs Semantics (Philosophical Distinctions)
Syntax vs Semantics (Philosophical Distinctions)
Published: 2015/09/20
Channel: Carneades.org
Syntax (logic)
Syntax (logic)
Published: 2016/01/22
Channel: WikiAudio
Python vs Visual Logic Syntax
Python vs Visual Logic Syntax
Published: 2017/07/18
Channel: Jason Wertz
Propositional Logic: Syntax, Part 3
Propositional Logic: Syntax, Part 3
Published: 2015/05/30
Channel: David Agler
Being, Univocity, & Logical Syntax
Being, Univocity, & Logical Syntax
Published: 2017/07/18
Channel: Philosophical Overdose
Predicate Logic Symbolization Summary
Predicate Logic Symbolization Summary
Published: 2007/04/17
Channel: jellologic
First Order Logic - Syntax and Semantics
First Order Logic - Syntax and Semantics
Published: 2013/03/06
Channel: Jarrar Courses
Propositional Logic: Syntax, Part 2
Propositional Logic: Syntax, Part 2
Published: 2015/05/30
Channel: David Agler
Java: Syntax, Runtime, and Logic Errors
Java: Syntax, Runtime, and Logic Errors
Published: 2013/01/31
Channel: Cameron Christensen
[Mathematical Linguistics] Predicate Logic Syntax
[Mathematical Linguistics] Predicate Logic Syntax
Published: 2016/05/30
Channel: TheTrevTutor
Vlogic: Syntax Trees
Vlogic: Syntax Trees
Published: 2014/01/30
Channel: Vlogic
Syntax, Logic, Runtime Errors in Java
Syntax, Logic, Runtime Errors in Java
Published: 2016/06/26
Channel: Brandan Jones
15) Errors -- Syntax, Runtime & Logic
15) Errors -- Syntax, Runtime & Logic
Published: 2014/07/09
Channel: Joseph Bolen
DM-18-First Order logic -Learn To write statements
DM-18-First Order logic -Learn To write statements
Published: 2016/04/25
Channel: GATE CS LECTURES BY GATE BOOK
Java Programming Tutorial 06 Syntax Errors and Logical Errors
Java Programming Tutorial 06 Syntax Errors and Logical Errors
Published: 2011/02/09
Channel: Gaute Michel Ferstad
SEM122 - Predicate Logic II
SEM122 - Predicate Logic II
Published: 2013/06/28
Channel: The Virtual Linguistics Campus
PGC Lectures: Programming Errors & Types, Syntax Error, Runtime Error, Logical Error
PGC Lectures: Programming Errors & Types, Syntax Error, Runtime Error, Logical Error
Published: 2017/01/09
Channel: Online Learners
Mod-01 Lec-16 Syntax of Propositional Logic
Mod-01 Lec-16 Syntax of Propositional Logic
Published: 2015/03/18
Channel: nptelhrd
[Natural Deductive Logic] Basic Syntax of PL || Lecture 2
[Natural Deductive Logic] Basic Syntax of PL || Lecture 2
Published: 2014/10/21
Channel: TheTrevTutor
FOL (First Order Logic)
FOL (First Order Logic)
Published: 2015/07/20
Channel: Francisco Iacobelli
Artificial intelligence 23 Syntax For Preposition Logic in Ai
Artificial intelligence 23 Syntax For Preposition Logic in Ai
Published: 2017/01/25
Channel: Sanjay Pathak
Mod-04 Lec-03 Syntax and Semantics of CTL
Mod-04 Lec-03 Syntax and Semantics of CTL
Published: 2013/02/15
Channel: nptelhrd
syntax runtime and logical Errors in c#
syntax runtime and logical Errors in c#
Published: 2016/01/31
Channel: Umar Tech
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
Subjects and predicates | Syntax | Khan Academy
Subjects and predicates | Syntax | Khan Academy
Published: 2016/08/23
Channel: Khan Academy
Steve Awodey: Mac Lane and Carnap
Steve Awodey: Mac Lane and Carnap's Logical Syntax of Language
Published: 2014/04/12
Channel: Logic and Foundations of Mathematics
Mod-01 Lec-22 Lecture-22-Syntax of First order Logic (FL)
Mod-01 Lec-22 Lecture-22-Syntax of First order Logic (FL)
Published: 2012/07/23
Channel: nptelhrd
5 - 2 - 6.2 Syntax-Introduction to Logic-Professor Mike Genesereth
5 - 2 - 6.2 Syntax-Introduction to Logic-Professor Mike Genesereth
Published: 2012/05/20
Channel: OpenCourseOnline
Mod-01 Lec-02 Lecture-02-Syntax of Propositional Logic
Mod-01 Lec-02 Lecture-02-Syntax of Propositional Logic
Published: 2012/07/23
Channel: nptelhrd
2 - 2 - 2.2 Syntax of Propositional Logic -Introduction to Logic-Professor Mike Genesereth
2 - 2 - 2.2 Syntax of Propositional Logic -Introduction to Logic-Professor Mike Genesereth
Published: 2012/05/02
Channel: OpenCourseOnline
2.2 Syntax of Propositional Logic
2.2 Syntax of Propositional Logic
Published: 2012/10/12
Channel: Daniel Junior
Lecture - 9 First Order Logic
Lecture - 9 First Order Logic
Published: 2008/04/30
Channel: nptelhrd
Lesson 6 0 1 Syntax for Propositional Logic Part I
Lesson 6 0 1 Syntax for Propositional Logic Part I
Published: 2016/09/19
Channel: Michael Gavin
Symbolic Logic Syntax, Semantics, and Proof
Symbolic Logic Syntax, Semantics, and Proof
Published: 2016/04/09
Channel: Jeffrey Hill
1-8: Syntax and Run-time Errors
1-8: Syntax and Run-time Errors
Published: 2012/02/01
Channel: Kent D. Lee
Mac Lane and Carnap’s Logical Syntax of Language 2005 10 11 awodey
Mac Lane and Carnap’s Logical Syntax of Language 2005 10 11 awodey
Published: 2017/07/20
Channel: kujif
M2 Lec 2 - Propositional Logic: Syntax and Truth Values
M2 Lec 2 - Propositional Logic: Syntax and Truth Values
Published: 2016/01/12
Channel: NOC16 Jan-May CS02
Java Errors: Little logic and syntax errors
Java Errors: Little logic and syntax errors
Published: 2017/02/07
Channel: Josiah L
Symbolic Logic Syntax, Semantics, and Proof
Symbolic Logic Syntax, Semantics, and Proof
Published: 2017/02/24
Channel: Rilo Kiley
Python Basics - 21 - Errors syntax, infinite, logical
Python Basics - 21 - Errors syntax, infinite, logical
Published: 2016/10/08
Channel: HYPED247
Program Development Process, Pseudocode, Syntax Error, Runtime Error, Logic Error
Program Development Process, Pseudocode, Syntax Error, Runtime Error, Logic Error
Published: 2017/05/20
Channel: Christian Hur
1-2 Discrete Mathematics - Propositional Logic - The Syntax of Propositional Logic
1-2 Discrete Mathematics - Propositional Logic - The Syntax of Propositional Logic
Published: 2015/10/13
Channel: yoitsfrancis
Error types Syntax,Run time and logical with Java [updated]
Error types Syntax,Run time and logical with Java [updated]
Published: 2015/05/20
Channel: Mohamed Khamis
Excel 2007 VBA Macro Development - Understanding Logic Errors and Syntax Errors
Excel 2007 VBA Macro Development - Understanding Logic Errors and Syntax Errors
Published: 2017/04/05
Channel: Free Books Online
Excel Logic Functions - IF, AND, and OR
Excel Logic Functions - IF, AND, and OR
Published: 2010/10/01
Channel: Ralph Phillips
Truth trees for propositional logic 1
Truth trees for propositional logic 1
Published: 2013/01/19
Channel: Kane B
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WIKIPEDIA ARTICLE

From Wikipedia, the free encyclopedia
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This diagram shows the syntactic entities which may be constructed from formal languages.[1] The symbols and strings of symbols may be broadly divided into nonsense and well-formed formulas. A formal language is identical to the set of its well-formed formulas. The set of well-formed formulas may be broadly divided into theorems and non-theorems.

In logic, syntax is anything having to do with formal languages or formal systems without regard to any interpretation or meaning given to them. Syntax is concerned with the rules used for constructing, or transforming the symbols and words of a language, as contrasted with the semantics of a language which is concerned with its meaning.

The symbols, formulas, systems, theorems, proofs, and interpretations expressed in formal languages are syntactic entities whose properties may be studied without regard to any meaning they may be given, and, in fact, need not be given any.

Syntax is usually associated with the rules (or grammar) governing the composition of texts in a formal language that constitute the well-formed formulas of a formal system.

In computer science, the term syntax refers to the rules governing the composition of well-formed expressions in a programming language. As in mathematical logic, it is independent of semantics and interpretation.

Syntactic entities[edit]

Symbols[edit]

A symbol is an idea, abstraction or concept, tokens of which may be marks or a configuration of marks which form a particular pattern. Symbols of a formal language need not be symbols of anything. For instance there are logical constants which do not refer to any idea, but rather serve as a form of punctuation in the language (e.g. parentheses). A symbol or string of symbols may comprise a well-formed formula if the formulation is consistent with the formation rules of the language. Symbols of a formal language must be capable of being specified without any reference to any interpretation of them.

Formal language[edit]

A formal language is a syntactic entity which consists of a set of finite strings of symbols which are its words (usually called its well-formed formulas). Which strings of symbols are words is determined by fiat by the creator of the language, usually by specifying a set of formation rules. Such a language can be defined without reference to any meanings of any of its expressions; it can exist before any interpretation is assigned to it – that is, before it has any meaning.

Formation rules[edit]

Formation rules are a precise description of which strings of symbols are the well-formed formulas of a formal language. It is synonymous with the set of strings over the alphabet of the formal language which constitute well formed formulas. However, it does not describe their semantics (i.e. what they mean).

Propositions[edit]

A proposition is a sentence expressing something true or false. A proposition is identified ontologically as an idea, concept or abstraction whose token instances are patterns of symbols, marks, sounds, or strings of words.[2] Propositions are considered to be syntactic entities and also truthbearers.

Formal theories[edit]

A formal theory is a set of sentences in a formal language.

Formal systems[edit]

A formal system (also called a logical calculus, or a logical system) consists of a formal language together with a deductive apparatus (also called a deductive system). The deductive apparatus may consist of a set of transformation rules (also called inference rules) or a set of axioms, or have both. A formal system is used to derive one expression from one or more other expressions. Formal systems, like other syntactic entities may be defined without any interpretation given to it (as being, for instance, a system of arithmetic).

Syntactic consequence within a formal system[edit]

A formula A is a syntactic consequence[3][4][5][6] within some formal system of a set Г of formulas if there is a derivation in formal system of A from the set Г.

Syntactic consequence does not depend on any interpretation of the formal system.[7]

Syntactic completeness of a formal system[edit]

A formal system is syntactically complete[8][9][10][11] (also deductively complete, maximally complete, negation complete or simply complete) iff for each formula A of the language of the system either A or ¬A is a theorem of . In another sense, a formal system is syntactically complete iff no unprovable axiom can be added to it as an axiom without introducing an inconsistency. Truth-functional propositional logic and first-order predicate logic are semantically complete, but not syntactically complete (for example the propositional logic statement consisting of a single variable "a" is not a theorem, and neither is its negation, but these are not tautologies). Gödel's incompleteness theorem shows that no recursive system that is sufficiently powerful, such as the Peano axioms, can be both consistent and complete.

Interpretations[edit]

An interpretation of a formal system is the assignment of meanings to the symbols, and truth values to the sentences of a formal system. The study of interpretations is called formal semantics. Giving an interpretation is synonymous with constructing a model. An interpretation is expressed in a metalanguage, which may itself be a formal language, and as such itself is a syntactic entity.

References[edit]

  1. ^ Dictionary Definition
  2. ^ Metalogic, Geoffrey Hunter
  3. ^ Dummett, M. (1981). Frege: Philosophy of Language. Harvard University Press. p. 82. ISBN 9780674319318. Retrieved 2014-10-15. 
  4. ^ Lear, J. (1986). Aristotle and Logical Theory. Cambridge University Press. p. 1. ISBN 9780521311786. Retrieved 2014-10-15. 
  5. ^ Creath, R.; Friedman, M. (2007). The Cambridge Companion to Carnap. Cambridge University Press. p. 189. ISBN 9780521840156. Retrieved 2014-10-15. 
  6. ^ "syntactic consequence from FOLDOC". swif.uniba.it. Retrieved 2014-10-15. 
  7. ^ Hunter, Geoffrey, Metalogic: An Introduction to the Metatheory of Standard First-Order Logic, University of California Pres, 1971, p. 75.
  8. ^ "A Note on Interaction and Incompleteness" (PDF). Retrieved 2014-10-15. 
  9. ^ "Normal forms and syntactic completeness proofs for functional independencies". portal.acm.org. Retrieved 2014-10-15. 
  10. ^ Barwise, J. (1982). Handbook of Mathematical Logic. Elsevier Science. p. 236. ISBN 9780080933641. Retrieved 2014-10-15. 
  11. ^ "syntactic completeness from FOLDOC". swif.uniba.it. Retrieved 2014-10-15. 

See also[edit]

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