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• Natural Language or NL refers to the common spoken or written language spoken by humans. More info at http://en.wikipedia.org/wiki/Natural_language
• Entity-Relational Language or ER refers to the language used mainly represent databases. More info at http://en.wikipedia.org/wiki/Entity_relationship
• UML or Unified Modeling Language is a modeling language used in software engineering to represent various architectural elements of a system. More info at http://en.wikipedia.org/wiki/Unified_Modeling_Language
• XML or eXtensible Markup Language is a language used to capture data and metadata mainly from documents. More info at http://en.wikipedia.org/wiki/XML

The main objective of a logic is to express, by means of a formal language, the knowledge about a certain phenomenon and encode with a precise set of rewriting rules (inference rules) the basic reasoning steps which are considered to be correct by everybody. A correct reasoning allows to show that a certain knowledge is a logical consequence of a given set of facts. Correct reasoning chains are constructed by concatenating applications of simple inference rules.

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• World: we have the photo of a monkey eating a banana on a tree
• Model: stylized representation of the monkey (i.e. the modeling simplified and filtered some elements from the world).
• Language+Theory: the scene is reduced by three texts, which are the name of the entities (Monkey and Banana) and the description of the action (MonkeEatsBanana).

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• PL or Propositional Logic is mainly used to derive theorems from a series of formulas. Example: P -> Q (and, or, then and not are some other relations available). More information at http://en.wikipedia.org/wiki/Propositional_logic
• FOL or First Order Logic (also known as predicate logic), uses quantifiers (like the “inverted A” which means “for all” and the “inverted E” which means “exists one”). More information at http://en.wikipedia.org/wiki/First-order_logic
• DL or Descriptive Logic: besides propositions (or concepts as they are known, DL also introduces Individuals and Roles. DL also introduces relationships like “equivalent”, “defined to be equal”, “is related”. More information at http://en.wikipedia.org/wiki/Description_logic

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An important note is about the difference between data and knowledge. Data can be thought as variables assuming different values, let's take dw=7 just for example; we miss the INFORMATION because no context is given. If I state that dw is the total number of days in a week, I immediately get the information that a week is composed by 7 days.

Essentially, knowledge is provided by a reasoning procedure about data and information.

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• The English data has the most straight forward description.
• In the Java description three “girl variables” are defined and a string representing their names is loaded into it.
• The diagram defines 3 circles representing the girls (with her names) and connects them to a concept box “GIRL”.
• In first order logic three propositions are created, each stating that one of the names is a girl.

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• English: the sentence that describes the action was simply appended at the beginning of the sentence.
• Java: the definition of girl was stream-lined by defining a “Girl class”. Furthermore the attribute “Playing” from the girl class is used to indicate with who the current girl instance is playing.
• Diagram: a parallelogram with the word “PLAY” was connected to “GIRL”, thus implying that “all girls play”.
• The First-order logic represents the addition by saying “For all x and y; if x is a girl and y is a girl, then they play together”

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