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Wikipage of Group 9

Overview

Members

Lisa
Marthe
Elisabeth
Isabelle

Short description of the topic

Predicate logic - logical connectives

"Predicate logic" is a linguistic concept belonging to the field of semantics, specifically syntax and grammar. Within that concept natural language is translated into a logical language (formulae) in order to illustrate the relation between a sentence, the conditions under which a given sentence is true and the circumstances in the real world.

The predicate of a sentence serves either to assign an information (property) to a single argument ("argument" here meaning a part of the sentence, such as subjects and objects) or to relate two or more arguments to each other. The predicate is seen as linking its arguments to give purpose to a sentence's content. Such a sentence can be paraphrased in a structured way which gives information about the relations between the elements of the sentence.

The purpose of Predicate logic is to avoid ambiguity in sentences by forming formulae out of natural language, which can only be interpreted in one way. Logical connectives, in form of symbols, are used to create formulae out of sentences with "and", "or", "if/then" and "not" and thereby giving information about the mentioned relations.

The aim is to be able to interpret given formulae in a way that it becomes possible to state if a given sentence is true or false regarding a given model or story that the formulae were formed from. A model in this case means the information given about all the individuals of a setting, their properties and their relations in the real world.

Connectives - Examples

AND

Symbol: Ʌ
Sentence: Harry is a student and Snape is a teacher.
Formulae: [[student(harry) Ʌ teacher(snape)]] = true/false

Truthtable AND

OR

Symbol: V
Sentence: Harry is a student or Snape is a teacher.
Formulae: [[student(harry) V teacher(snape)]] = true/false

Truthtable OR

IF/THEN

Symbol: -->
Sentence: If Harry is a student then Snape is a teacher.
Formulae: [[student(harry) --> teacher(snape)]] = true/false

Truthtable IF/THEN

NOT

Symbol: ¬
Sentence: Harry is not a student.
Formulae: [[¬student(harry)]] = true/false

The original formulae has to be false, that the overall statement is true.

Example: Only if student(harry) is false, ¬student(harry) is true.

Truthtable NOT

Difficulties

Abstraction of content/natural language
Understanding the whole process from creating a model to interpret formulae
Understanding the truth conditions of a formulae with connectives

References and links

References

Course material "Introduction to Semantics" by Manfred Sailer
Levine, Robert D., Frank Richter, and Manfred Sailer (in preparation): Formal Semantics. An Empirically Grounded Approach. Stanford: CSLI Publications. Draft of April 2012.