[paper reading][New Generation Computing 1986] A Logic-based Calculus of Events

目录

• 1 Introduction
• 2 A Simplified Example
• 3 The Promotion Example in Detail
• 4 Execution of the Promotion Example
• 5 Incompleteness and Incorrectness of Start and End
• 12 Conclusion

• New Generation Computing 1986
• https://www.doc.ic.ac.uk/~rak/papers/event calculus.pdf
• use formal logic to formalize the notion of time (Horn clause subset of classcal logic)

1 Introduction

• situation calculus, global
• event calculus, local events and time periods

2 A Simplified Example

• hire, left, update, knowledge
• figure
  
• sometimes, the end of a period after(e) (e is a certain time instant) is undifined but might be determined by means of additional information later
• end of lectureship, begin of professorship
• proof after(\(E_1\)) = before(\(E_4\)), i.e. combine "*-- and --*" to "*--*"?
  • *--*--* structure, "complete"
  • derived by a rule expresses ... 'cannot': negation, non-monotonic
    
• another rule
  
  • aim to find Mary's rank at a time instant using the mentioned rules.
• general characteristics of the EC approach
  • add, not delete ("no longer"? we explicitly show the end)
    • in contrast, conventional database systems, arbitrary.
    • EC: an extra level of semantic structure (inductive bias)
  • Past and Future are treated symmetrically. independent of the order. incomplete, with new knowledge, with hypothetical possibilities.
    • conventional: integrity constraint, statement
  • relative ordering, numerical? not essential.
  • concurrent
  • duration, now pictured
    
    • not wholly contained
  • equivalence preserving, PROLOG
  • situation calculus, global, frame problem, computationally inefficient. EC: local, different names even if they have the same duration
  • periods rather than on time instants
  • sacrifice conciseness for expressiveness, modal logic

3 The Promotion Example in Detail

• an exemplar rule: Rank(person, position, after(instant)) if Hire(person, position, instant)
• assume complete now (even though an incomplete description would be more natural)
• general rule, same rank, <, not disjoint, "Temp" means domain specific.
  • axiom: same relationship: identical or disjoint
  • disjoint: < or =!
• rule for the notion of disjoint
• end, start, same, sabattical (so the notion of disjoint contains '=')
• interpret the negative condition?

4 Execution of the Promotion Example

• PROLOG, infinite
• try to solve..., so try to solve..., loop
• intelligent solver or transformation techniques

5 Incompleteness and Incorrectness of Start and End

• Negation by failure is a form of the closed world assumption, that the "knowledge base" is complete:

not p is judged to hold if all ways of showing p fail

• start, end, incomplete, incorrect
• some event, not reported, occured
• rely on the completeness of 'start' and 'end', incorrect
• additional rule, solve the incorrectness before incompleteness

12 Conclusion

• events, primitive
• conflict, non-monotonically withdrawn
  • conventional: reject. only appropriate when ordered
  • extension, "Mary was a professor when Jim was promoted"