diff --git a/ContextAlgebra.cabal b/ContextAlgebra.cabal --- a/ContextAlgebra.cabal +++ b/ContextAlgebra.cabal @@ -10,13 +10,13 @@ -- PVP summary: +-+------- breaking API changes -- | | +----- non-breaking API additions -- | | | +--- code changes with no API change -version: 0.1.0.0 +version: 0.2.0.0 -- A short (one-line) description of the package. synopsis: Context Algebra -- A longer description of the package. -description: Context Algebra to identify typical exemplars of a concept influenced by a context. +description: Context Algebra to identify typical exemplars of a concept influenced by a context. A executable model is included in the package NearContextAlgebra also available here -- The license under which the package is released. license: BSD3 @@ -25,7 +25,7 @@ license-file: LICENSE -- The package author(s). -author: juergenhah +author: Jürgen Hahn -- An email address to which users can send suggestions, bug reports, and -- patches. @@ -48,7 +48,7 @@ library -- Modules exported by the library. - exposed-modules: Model, ContextLattice + exposed-modules: ConceptModel, ContextLattice -- Modules included in this library but not exported. -- other-modules: diff --git a/src/ConceptModel.hs b/src/ConceptModel.hs new file mode 100644 --- /dev/null +++ b/src/ConceptModel.hs @@ -0,0 +1,144 @@ +{-# LANGUAGE DefaultSignatures #-} +{-# LANGUAGE FlexibleContexts #-} +{-# LANGUAGE MultiParamTypeClasses #-} +{-| +Module : ConceptModel +Description : connects the context Lattice with observation frequencies of exemplars using a multiset +Maintainer : hahn@geoinfo.tuwien.ac.at +Stability : beta + +This module implements the necessary functions to model a concept influenced by several contexts. The concept is represented by several exemplars. For each influencing context the exemplars have different observation frequency. The connection from exemplars and context is modeled by the data type Experience. Each Experience can be made several times where the amount is hold by a Multiset. +-} +module ConceptModel (Experience(..) + , Concept(..) + , Probability + ,ConceptContextModel + ,createConceptForContext + ,typicalityForExemplarsInContext + ,typicalExemplarInContext + ,printConcept + ,unionsConceptsForDiffContexts + ,filterConceptWithContext + ,amountExperiences) where + +import ContextLattice + +import Algebra.Enumerable +import qualified Data.Function as F +import qualified Data.List as L +import qualified Data.MultiSet as Mset + +-- | Each experience is formed by a exemplar of type e and a context c this exemplar was observed at. +data Experience c e = + -- | constructor; establishes an experience from a context and an exemplar + Exp c e deriving (Ord, Show, Eq) + +-- | All experiences are hold in a multiset +type Concept c e = Mset.MultiSet (Experience c e) + +-- | type synonym for better readability +type Probability = Float + +-- | the class defines the necessary functions needed for the context algebra +class (Ord c, Ord e, Show c, Show e)=> ConceptContextModel c e where + + -- | combines the observation amount of exemplars for one context + createConceptForContext :: (Show c,Ord c, Show e,Ord e) => + (Context c) -- ^ context in which the experiences were made + -> [e] -- ^ exemplars which are observed + -> [Int] -- ^ amount of observations for one exemplar in this context + -> Concept (Context c) e -- ^ resulting concept with the given experiences + createConceptForContext context exemplars amounts = Mset.unions $zipWith manyfoldExperiences experiencesOnce amounts + where experiencesOnce = map (Exp context) exemplars + + -- | If an experience is made several times the amount can be specified by the @amount@ + manyfoldExperiences :: (Ord c, Show c, Ord e, Show e) => + Experience (Context c) e -- ^ experience that is observed several times + -> Int -- ^ amount of observations of the experience + -> Concept (Context c) e -- ^ concept represented by an amount of experiences + manyfoldExperiences exp amount= Mset.insertMany exp amount Mset.empty + + -- | calculates the amount of experiences that are present for the concept + amountExperiences :: + Concept (Context c) e -- ^ concept including experinces + -> Int -- ^ amount of experiences + amountExperiences = Mset.size + + -- | unions the experiences stored for one concept for different contexts + unionsConceptsForDiffContexts :: (Ord e, Ord c) => + [Concept (Context c) e] -- ^ list of conceptualizations holding experiences for different contexts + -> Concept (Context c) e -- ^ union of the experiences holding now all experiences for all contexts + unionsConceptsForDiffContexts = Mset.unions + + -- | filters a concept for a context, gets a concept for a finer context, + -- the context c has to be more finer than the context that are included in the concept + filterConceptWithContext :: ((Enumerable c), Enumerable (Context c),Ord e, Eq c,Ord c) => + Context c -- ^ context used to filter the experiences + -> Concept (Context c) e -- ^ experiences to filter + -> Concept (Context c) e -- ^ filtered experiences, more finer experiences are returned + filterConceptWithContext context concept = Mset.unions . L.map (\fctx -> (Mset.filter (\(Exp c1 _)-> c1 == fctx ) concept ) ) $ allfinerContexts + where allfinerContexts = getFinerContexts context + + + -- | returns a probability of an exemplar observed in a context for the given experiences + typicalityofExemplarInContext ::((Enumerable c), Enumerable (Context c),Ord e,Ord c)=> + Experience (Context c) e -- ^ exemplar and context to look for + -> Concept (Context c) e -- ^ concept hoding experiences that are considered + -> Probability -- ^ probability of the exemplar in this context for the given concept + typicalityofExemplarInContext (Exp context exemplar) concept = if amountContext==0 then 0 + else amountExemplar /amountContext + where observationAmounttForContext = amountExperiences experiencesForContext; + exemplarOservationAmountForContext = amountExperiences $ filterExemplars exemplar experiencesForContext; + experiencesForContext = filterConceptWithContext context concept + amountExemplar= fromIntegral exemplarOservationAmountForContext + amountContext = fromIntegral observationAmounttForContext + + -- * functions to print and export + -- | returns the typicality distribution for each exemplar in the context c, the type e is only used as type parameter + typicalityForExemplarsInContext :: (Ord c, Ord e,Enum e,Bounded e,(Enumerable c), Enumerable (Context c))=> + Context c -- ^ context the distribution is made for + -> e -- ^ exemplar type, used as type parameter + -> Concept (Context c) e -- ^ concept with the experiences + -> [(e,Probability)] -- ^ returned distribution + typicalityForExemplarsInContext context exemplar concept= map (\e ->(e, typicalityofExemplarInContext (Exp context e) concept) ) exemplars + where exemplars= enumFromTo minBound $ maxBound `asTypeOf` exemplar + + -- | returns the typical exemplar of a concept for the context + typicalExemplarInContext :: (Ord c, Ord e,Enum e,Bounded e,(Enumerable c), Enumerable (Context c))=> + Context c -- ^ context the distribution is made for + -> e -- ^ exemplar type, used as type parameter + -> Concept (Context c) e -- ^ concept with the experiences + -> (e, Probability) -- ^ tupel with the highest probability value + typicalExemplarInContext context exemplar concept = L.maximumBy (compare `F.on` snd) $ typicalityForExemplarsInContext context exemplar concept + + + -- | returns experiences for the exemplar given in the first argument @e@ + -- in quantum mechanics called projector + filterExemplars:: (Ord c, Ord e) => + e -- ^ exemplar used to filter the experiences + -> Concept (Context c) e -- ^ concept that are filtered + -> Concept (Context c) e -- ^ concept including experiences for the exemplar e + filterExemplars exemplar = Mset.filter (\(Exp _ actualExemplar)-> exemplar ==actualExemplar) + + + -- | converts the experiences of the concept to a IO() + printConcept :: (Show e, Show c) => + Concept c e -- ^ experiences of the concept to print + -> IO() -- ^ returned IO() + printConcept concept = putStrLn $ Mset.showTreeWith True True concept + + + -- * functions for further development of the model + -- | adds the @new@ experience to the given experiences + addExperience :: (Ord c,Ord e) => + Experience c e -- ^ new experience to add + -> Concept c e -- ^ given concept where to add the new experience + -> Concept c e -- ^ resulting concept including the new and the given experiences + addExperience = Mset.insert + + + forgetExperience:: (Ord c,Ord e) => + Experience c e -- ^ new experience to add + -> Concept c e -- ^ given concept where to add the new experience + -> Concept c e -- ^ resulting concept including the new and the given experiences + forgetExperience = Mset.delete diff --git a/src/ContextLattice.hs b/src/ContextLattice.hs --- a/src/ContextLattice.hs +++ b/src/ContextLattice.hs @@ -110,6 +110,20 @@ propAssociative x y z = x `meet` (y `meet` z) == (x `meet` y) `meet` z +-- |Absorption laws +-- +-- @ +-- a `join` (a `meet` b) = a, +--a `meet` (a `join` b) = a. +-- @ + +-- | Identity laws +-- +-- @ +-- a `join` 0 = a, +-- a `meet` 1 = a. +-- @ + -- * not needed -- | checks in which level of the lattice the actual @Context c@ is -- One gets level 1, Zero gets level 0, and all others are 1+ diff --git a/src/Model.hs b/src/Model.hs deleted file mode 100644 --- a/src/Model.hs +++ /dev/null @@ -1,117 +0,0 @@ -{-# LANGUAGE FlexibleContexts #-} -{-# LANGUAGE MultiParamTypeClasses #-} -{-| -Module : Model -Description : connects the context Lattice with observation frequencies of exemplars using a multiset -Maintainer : hahn@geoinfo.tuwien.ac.at -Stability : beta - -This module implements the necessary functions to model a concept and the context influence. The concept is represented by several exemplars. For each influencing context the exemplars have different observation frequency. This conncetion is modeled here by a multiset. --} -module Model where - -import ContextLattice - -import Algebra.Enumerable -import qualified Data.Function as F -import qualified Data.List as L -import qualified Data.MultiSet as Mset - --- | Each experience is formed by a exemplar of type e and a context c this exemplar was observed at. -data Experience c e = - -- | constructor; establishes an experience from a context and an exemplar - Exp c e deriving (Ord, Show, Eq) - --- | All experiences are hold in a multiset -type Experiences c e = Mset.MultiSet (Experience c e) - --- | type synonym for better readability -type Probability = Float - --- | the class defines the necessary functions needed for the context algebra -class (Ord c, Ord e, Show c, Show e)=> InterpretationModel c e where - --- | combines the observation amount of exemplars for one context -createExperiencesForContext :: (Show c,Ord c, Show e,Ord e) => - c -- ^ context in which the experiences were made - -> [e] -- ^ exemplars which are observed - -> [Int] -- ^ amount of observations for one exemplar in this context - -> Experiences c e -- ^ resulting experience type -createExperiencesForContext context exemplars amounts = Mset.unions $zipWith manyfoldExperiences experiencesOnce amounts - where experiencesOnce = map (Exp context) exemplars - --- | If an experience is made several times the amount can be specified by the @amount@ -manyfoldExperiences :: (Ord c, Show c, Ord e, Show e) => - Experience c e -- ^ experience that is observed several times - -> Mset.Occur -- ^ amount of observations of the experience - -> Experiences c e -- ^ experiences with the given amount and type -manyfoldExperiences exp amount= Mset.insertMany exp amount Mset.empty - --- | calculates the amount of experiences that are present -amountExperiences :: - Experiences (Context c) e -- ^ experinces to be counted - -> Int -- ^ amount of experiences -amountExperiences = Mset.size - --- | filters experiences for a context, gets experiences for a finer context, --- the context c has to be more finer than the context that are included in the experiences -lambda :: ((Enumerable c), Enumerable (Context c),Ord e, Eq c,Ord c) => - Context c -- ^ context used to filter the experiences - -> Experiences (Context c) e -- ^ experiences to filter - -> Experiences (Context c) e -- ^ filtered experiences, more finer experiences are returned -lambda context experiences = Mset.unions . - L.map (\fctx -> (Mset.filter (\(Exp c1 _)-> c1 == fctx ) experiences ) ) $ allfinerContexts - where allfinerContexts = getFinerContexts context - --- | returns a probability of an exemplar observed in a context for the given experiences -mu ::((Enumerable c), Enumerable (Context c),Ord e,Ord c)=> - Experience (Context c) e -- ^ exemplar and context to look for - -> Experiences (Context c) e -- ^ experiences that are considered - -> Probability -- ^ probability of the exemplar in this context for the given experiences -mu (Exp context exemplar) experiences = if amountContext==0 then 0 - else amountExemplar /amountContext - where observationAmounttForContext = Mset.size experiencesForContext - exemplarOservationAmountForContext = Mset.size $ filterExemplars exemplar experiencesForContext - experiencesForContext = lambda context experiences - amountExemplar= fromIntegral exemplarOservationAmountForContext - amountContext = fromIntegral observationAmounttForContext - --- | returns experiences for the exemplar given in the first argument @e@ --- in quantum mechanics called projector -filterExemplars:: (Ord c, Ord e) => - e -- ^ exemplar used to filter the experiences - -> Experiences c e -- ^ experiences that are filtered - -> Experiences c e -- ^ experiences including values for the exemplar e -filterExemplars exemplar = Mset.filter (\(Exp _ actualExemplar)-> exemplar ==actualExemplar) - - --- * functions to print and export --- | returns the observation distribution for the context c, the type e is only used as type parameter -probAllExemplars4Context :: (Ord c, Ord e,Enum e,Bounded e,(Enumerable c), Enumerable (Context c))=> - Context c -- ^ context the distribution is made for - -> e -- ^ exemplar type, used as type parameter - -> Experiences (Context c) e -- ^ experiences the distribution is made of - -> [(e,Probability)] -- ^ returned distribution -probAllExemplars4Context ctx e t= map (\e ->(e, mu (Exp ctx e) t) ) exemplars - where exemplars= enumFromTo minBound $ maxBound `asTypeOf` e - --- | returns the most probable exemplar given by the list of tuples of (Exemplar, Probability) -getMostProbableExemplar :: (Ord e)=> - [(e, Probability)] -- ^ list of tupels of Exemplars and the probability value - -> (e, Probability) -- ^ tupel with the highest probability value -getMostProbableExemplar = L.maximumBy (compare `F.on` snd) - --- | converts the experiences type to a IO() -printExperiences :: (Show e, Show c) => - Experiences c e -- ^ experience to convert to IO - -> IO() -- ^ returned IO() -printExperiences experiences = putStrLn $ Mset.showTreeWith True True experiences - - --- * functions for further development of the model --- | adds the @new@ experience to the given experiences -addExperience :: (Ord c,Ord e) => - Experience c e -- ^ new experience to add - -> Experiences c e -- ^ given experiences where to add the new experience - -> Experiences c e -- ^ resulting experiences including the new and the given experiences -addExperience = Mset.insert