Department of Computer Science

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Department of Computer Science Engineering
University of California, San DiegoCSE-291
Ontologies in Data and Process IntegrationSpring
2004

• Bertram Ludäscher
• LUDAESCH_at_SDSC.EDU

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A riddle
This thing all things devours Birds, beasts,
trees, flowers Gnaws iron, bits steel Grinds
hard stones to meal Slays king, ruins town, And
beats high mountains down.
J. R. R. Tolkien, The Hobbit
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Time!
Ticking away the moments that make up the dull
day You fritter and waste the hours in an off
hand way Kicking around on a piece of ground in
your home town Waiting for someone or something
to show you the way Tired of lying in the
sunshine staying home to watch the rain You are
young and life is long and there is time to kill
today And then one day you find that ten years
have got behind you No one told you when to run,
you missed the starting gun And you run and run
to catch up with the sun, but it's sinking And
racing around to come up behind you again The sun
is the same in a relative way, but you're
older Shorter of breath and one day closer to
death Every year is getting shorter, never seem
to find the time Plans that either come to naught
or a half page of scribbled lines Hanging on in a
quiet desperation is the English way The time is
gone the song is over, thought I'd something more
to say
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Outline

• Temporal Databases and Statelog
• Introduction to Modal Logic
• Modal Logic, James Garson, Stanford Encyclopedia
  of Philosophy
• Introduction to Temporal Logic
• Temporal Logic, Antony Galton, Stanford
  Encyclopedia of Philosophy

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Active Databases Events, Conditions, Actions
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Event-Condition-Action (ECA) Rules
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Example
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Events
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Primitive Events
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Composite/Complex Events
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Event Consumption Modes
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Conditions
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Actions
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Example using Logic Rules
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Basic Statelog Execution Model
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Statelog Syntax
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Reified Syntax
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First-Order Predicate Logic Semantics
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Statelog Semantics
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Statelog Semantics
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Temporal Semantics
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Statelog Rules in Temporal Logic
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Refined Execution Model

• With this
• Programming change
• and reasoning about ..
• Termination
• Expressiveness
• complexity

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Application Examples
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Modal Logic

• Modal
• expressions (like necessarily or possibly) to
  qualify the truth of a judgement
• Modal logic
• study of the deductive behavior of the
  expressions it is necessary that and it is
  possible that
• a family of logics for belief, for tense and
  other temporal expressions, for the deontic
  (moral) expressions such as it is obligatory
  that and it is permitted that,
• Use for formal analysis of philosophical
  argument, where expressions from the modal family
  are both common and confusing

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What is Modal Logic?
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Possible World Semantics

• Def. Kripke Frame (G, R)
• Set of possible worlds G
• Binary Accessibility Relation R
• Propositional Kripke Structure K (G, R, v)
• v is a valuation function v P x G ? True,
  False
• mapping each proposition p ( 0-ary predicate)
  in P to either True or False, depending on the
  world g in G

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Formula Evaluation in Kripke Structures
Given Kripke Structure K (G, R, v), define
iff v(g,p) true iff g F and g H iff g
F or g H iff (not g F) or g H iff
not g F iff for all h s.t. R(g,h) h F iff
for some h s.t. R(g,h) h F
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Correspondence Theory for Propositional Modal
Logic
Linking the structure of R to valid formulas
Properties of R
characterizing axioms
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Modal Logic Primer

• Modal Logic
• Stanford Encyclopedia of Philosophy
• James Garson
• http//plato.stanford.edu/entries/logic-modal/

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Temporal Logic Primer

• Temporal Logic
• Stanford Encyclopedia of Philosophy
• Antony Galton
• http//plato.stanford.edu/entries/logic-temporal/