Visual Programming Languages ICS 539 Visual Logic Programming J. Augsti, et. All

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Visual Programming LanguagesICS 539Visual
Logic ProgrammingJ. Augsti, et. All A. Visual
Syntax.J. of Visual Languages and Computing,
1998 9, 399-427

• ICS Department
• KFUPM
• Feb. 1, 2005

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Introduction

• The increasing power of computers and the
  improvement of their graphical interfaces has
  fostered the development of visual programming.
• This, coupled with the interest in logic
  programming, naturally led researchers to devise
  various declarative programming languages.

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Visual Logic Programming
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Visual Logic

• The visual logic presented in this paper is based
  on two key ideas
• 1) Predicates are presented by means of graphical
  sets (labeled boxes) denoting set abstractions
  over the predicates.
• The intended meaning of the predicate is
  described by means of graphical set inclusions
  (box containment) which denote the inclusion of
  the corresponding set abstractions.
• For example, the following diagram describes the
  predicate mortal by saying that every human is
  mortal

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Example

• The diagram denotes the inclusion of the set
  abstractions corresponding to each labeled box

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• 2) Predicate application are represented by means
  of arrows which together with boxes form directed
  acyclic graphs (DAGs). These DAGs correspond to
  the structured terms of logic. For instance, the
  simple DAG

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• which translated to the textual form
• parent(human) the parents of some human
• denotes the following set abstraction
• where the parents y are represented by the
  contents of the parent box.

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• These two kinds of visual metaphors can be
  combined.
• For example, the following diagram defines the
  predicate grandparent

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• It says that the parents of the parents of
  someone (a variable element represented by a
  circle) are his/her grandparents, and denotes the
  following inclusion
• and the textual form of the diagram is

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• The key point of this visual syntax for logic is
  to represent visually the predicates as the set
  of elements that satisfy them, i.e. the set
  abstractions over them.
• Then inclusion of these sets corresponds to
  logical implication between set abstraction
  formulas, thus allowing an intuitive graphical
  representation of implication.

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• For example, the previous diagram defining the
  grandparent relation can be considered a
  visualization of the following implication

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Visual Terms

• We have two types of visual terms
• 1) Element visual terms which denote individuals
  or elements of the universe of discourse. They
  are either
• A circle representing a variable element.
• A labeled round box representing a constant
  element.
• A labeled round box with n incoming arrows
  representing a function of arity n where each
  arrow is applied to another element visual term.

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Example - Element visual term
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Set Visual Terms

• Set visual terms which denote sets of elements of
  the universe of discourse. They are either
• A labeled rectangular box denoting the set
  corresponding to the unary predicate named by the
  label.
• A labeled rectangular box with n incoming arrows
  representing a predicate of arity n, where each
  arrow is applied to an element visual term or a
  set visual term.

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• An unlabeled box containing two set visual term
  roots, which denotes the union of the sets
  corresponding to these visual terms.
• An unlabeled box shared by two set visual term
  roots, both containing it. This denotes the
  intersection of the sets corresponding to these
  visual terms.
• A gray box linked by a line to the root of a set
  visual term. It denotes the set complementary to
  the set of the visual term.

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Visual Constructs
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Example Set Visual Terms
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Visual Formulas (Diagrams)

• The goal of diagrams is to define logical
  predicates or relations.
• In every diagram there is a distinguished set
  term called the goal set term, which is an
  application to element terms of the predicate we
  want to define.
• To define a set term we indicate which are its
  elements, giving either the elements explicitly
  or a set term included in it.
• The goal set term is marked by drawing its box
  using thick lines.

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Example

• Figure 6 shows an example of how diagrams are
  constructed.
• First, in diagrams (a)-(c), we give different
  cases that satisfy the parent relation (the
  parents of Peter, Johnand Mary).
• Next, in diagrams (d) and (e) of the same figure
  we define the ancestor relation.
• In the first diagram, we state that parents are
  ancestors and in diagram (e) we formulate the
  recursive case the ancestors of the parents of x
  are also ancestors of x.
• The last example, diagram (f ), defines
  descendant, the symmetric relation of ancestor.
  Note that this one is a diagram with two
  inclusions, one being the conclusion and the
  other the condition.

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Example

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• If we translate to FOL the diagrams in Figure 6,
  with all variables implicitly universally
  quantified

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