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Two topics

Dive into a theory of space rooted in cartography, understand mathematical foundations, and explore IKL logic for seamless information exchange and interoperability in formal systems.

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Two topics

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  1. Two topics Pat Hayes Florida IHMC

  2. (old) (academic) stuffA theory of space based on cartography • What mathematical model of space underlies our models? • Take one off the mathematical shelf (R3, topology, metric space, tolerance space…??) • Try to make the fewest assumptions compatible with being able to do what needs to be done … … which in Geo applications is, to be able to represent it by a map.

  3. (old) (academic) stuffA theory of space based on cartography • To represent a space by a map. • This rules out topology (!) since we can map a continuous space using a discrete pixel screen. • Assume a set of ‘locations’ with two relations < part-of d part-of-boundary • Basic axioms: any set of locations has aunique minimal covering location; any boundary part is the boundary of two non-overlapping locations (the ‘sides’) • Map semantics theory based on this can support a large variety of intuitive mapping conventions, eg chloropleth maps, sketch maps, metro maps, driving directions, projections.

  4. (new) (not academic) stuffIKL logic for information interchange • Based on ISO Common Logic (CL) which is itself highly flexible • No distinction between class, relation, individual names • Any term can denote a relation • Can quantify over relations (but is first order) • IKL allows any name to be used in any logical way. Fosters interoperability by removing need to negotiate between uses. • IKL can describe its own naming conventions and relate them to others • IKL has names for its own propositions. So it can describe classes of propositions, variant or contextual truth-conditions for sentences, etc..

  5. (new) (not academic) stuffIKL logic for information interchange • Many barriers to interoperation are artifacts of the inflexibility of our formalisms rather than real conceptual misalignments. (Examples: class/individual or individual/property distinctions in DLs and other ‘conventional’ first-order notations; extensional vs. intensional uses of names; continuants vs. occurrents in describing time and change; modalities vs. parameters) IKL can reduce all of these to simple conversion axioms, all written in IKL, and can relate them to particular notational frameworks. • (CapitalCity UK London 1999)(holds (= (CapitalCity UK) London) 1999)(= (CapitalCity (UK 1999)(London 1999)))((CapitalCity UK London) 1999)(timeDurationOfProposition 1999 (that (CapitalCity UK London))) • (forall ((x timeInterval) y …)(iff (y … x)((y …) x) ))

  6. (new) (not academic) stuffIKL logic for information interchange • (exists ((x Iranian)) (believes Mary (that(and (customer x "Bank Melli Iran") (exists 3 ((y aircraft))(owns x y)))) ))

  7. (new) (not academic) stuffIKL logic for information interchange • Almost any (any?) current KR formalism can be straightforwardly translated into IKL. • OWL (DL) sentences become IKL terms denoting properties: • (= USTripleParent (AND Person (ATLEAST 3 childOf) (ALLARE childOf (SOMEARE attends (AND School (IS locatedIn USA)))))) ) • <owl:Class rdf:ID="#USTripleParent">   <owl:intersectionOf rdf:parseType="Collection">     <owl:Class rdf:about="#Person" />     <owl:Restriction>       <owl:onProperty rdf:resource="#childOf" />       <owl:minCardinality rdf:datatype="&xsd;nonNegativeInteger">3</owl:minCardinality>     </owl:Restriction>    <owl:Restriction>       <owl:onProperty rdf:resource="#childOf" />       <owl:allvaluesFrom>         <owl:Restriction>           <owl:onProperty rdf:resource="#attends" />             <owl:someValuesFrom>             <owl:intersectionOf rdf:parseType="Collection">                <owl:Class rdf:about="#School" />             <owl:Restriction>              <owl:onProperty rdf:resource="#locatedIn" />             <owl:hasvalue rdf:resource="#USA" />               </owl:Restriction>              </owl:intersectionOf>           </owl:someValuesFrom>         </owl:Restriction>       </owl:allValuesFrom>     </owl:Restriction>   </owl:intersectionOf> </owl:Class>

  8. (new) (not academic) stuffIKL logic for information interchange • Context logics transcribe directly, but opaque names are represented in IKL by contextualized names, eg (‘The Prince’ Context2453-A)allowing hypotheses about identity to beexpressed directly: • (= (‘The Prince’ Context2453-A) “Osama bin Laden”)

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