Glossary: Logical Connectives: Difference between revisions
No edit summary |
|||
| (9 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
{{MaterialUnderConstruction}} | {{MaterialUnderConstruction}} | ||
{{CreatedByStudents1213}} ''Involved participants: [[User:Lisa| Lisa]], [[User:Marthe| Marthe]], [[User:Elisabeth.krall| Elisabeth]], [[User:IsaB|Isabelle]].'' | |||
| Line 6: | Line 8: | ||
== Definition == | == Definition == | ||
Logical connectives are the conjunction ''and'', the disjunction ''or'', | Logical connectives are | ||
* the conjunction ''and'' (∧), | |||
* the disjunction ''or'' (∨), | |||
* the implication ''if...then...'' (⊃), | |||
* the equivalence (or: bi-implication) ''if and only if'' (⇔), | |||
* the negation ''not'' (¬) | |||
They are used in order to connect atomic formulae in logical language, i.e. atomic sentences in natural language. | |||
== Examples == | == Examples == | ||
The following examples refer to the scenario given in | The following examples refer to the scenario given in an [[Exercise_First_Order_Models|online exercises]]. | ||
Sentence: ''Paul rather wants to live in Munich and Alice is small.''<br />Complex formula: '''wants-to-live-in-Munich'''('''paul''') ∧ '''small'''('''alice''') | |||
Complex formula: '''dog (walter) | Sentence: ''Walter is a dog or Tom is not blonde.''<br />Complex formula: '''dog'''('''walter''') ∨ ¬'''blonde'''('''tom''') | ||
== References == | == References == | ||
* [[ | * [[Wiki-ch2#Truth_tables| Truth tables for logical connectives]] | ||
== Literature == | == Literature == | ||
* Levine, Robert D., Frank Richter, and Manfred Sailer (in preparation): Formal Semantics. An Empirically Grounded Approach. Stanford: CSLI Publications. Draft of April 2012. Chapter 2. | * Levine, Robert D., Frank Richter, and Manfred Sailer (in preparation): Formal Semantics. An Empirically Grounded Approach. Stanford: CSLI Publications. Draft of April 2012. Chapter 2. | ||
<hr /> | |||
Back to the [[Basic_Glossary|glossary]]. | |||
Latest revision as of 15:45, 11 April 2013
Warning:
The material on this page has been created as part of a seminar. It is still heavily under construction and we do not guarantee its correctness. If you have comments on this page or suggestions for improvement, please contact Manfred Sailer.
This note will be removed once the page has been carefully checked and integrated into the main part of this wiki.
The following material is an adapted form of material created by student participants of the project e-Learning Resources for Semantics (e-LRS). Involved participants: Lisa, Marthe, Elisabeth, Isabelle.
Logical Connectives
Definition
Logical connectives are
- the conjunction and (∧),
- the disjunction or (∨),
- the implication if...then... (⊃),
- the equivalence (or: bi-implication) if and only if (⇔),
- the negation not (¬)
They are used in order to connect atomic formulae in logical language, i.e. atomic sentences in natural language.
Examples
The following examples refer to the scenario given in an online exercises.
Sentence: Paul rather wants to live in Munich and Alice is small.
Complex formula: wants-to-live-in-Munich(paul) ∧ small(alice)
Sentence: Walter is a dog or Tom is not blonde.
Complex formula: dog(walter) ∨ ¬blonde(tom)
References
Literature
- Levine, Robert D., Frank Richter, and Manfred Sailer (in preparation): Formal Semantics. An Empirically Grounded Approach. Stanford: CSLI Publications. Draft of April 2012. Chapter 2.
Back to the glossary.