def proveSequent(C6, bfactlist, bgoal) :
"""attempts to prove proposition bgoal from sequence of propositions
bfactlist.
params: C6; bfactlist - sequence of btrees; bgoal - a btree
Approach: places bgoal into cnf;
places conjucntion of bfactlist into dnf;
for each subgoal in cnf, for each sublist in dnf,
attempts to prove sublist |- subgoal.
If all are accomplished, then goal is proved.
returns True, if bgoal proved; returns False otherwise
"""
#if bgoal[0] == "forall" :
# success = proveUniversal(C6, bfactlist, bgoal) # sorry...
# return success
# place bfactlist into dnf to compute all possible proof contexts:
bigfact = NF.conjunctionOf(bfactlist)
dfacts = NF.dnf(bigfact) # all possible cases in bfactlist
subgoals = NF.cnf(bgoal) # must prove all subgoal conjuncts
for subg in subgoals : # must prove each subgoal, subg
if ["True"] in subg : # each subg is a disjunct...
pass # it's proved
else :
for premiselist in dfacts : # must prove each premiselist |- subg
#print "READY TO PROVE:", premiselist
#print "|-", subg
#print
if ["False"] in premiselist :
pass # proved -- the premises are self-contradictory
else : # rats, time to do a proof:
# since subg is a disjunction, use premiselist
# to try to prove _one_ of the disjuncts:
proved_subg = False
for prim in subg :
proved_subg = verifyRelation(C6, premiselist, prim)
if proved_subg : break
if not(proved_subg) : return False # we failed
return True # we made it this far; it means all subgoals were
def insertRelation(C6, btree):
"""extracts all [RELOP, e1, e2]-relations asserted within btree
and places them into the rels table in C6
params: C6 table and btree
"""
#sigma = C6["store"]
# eval all facts in the bfactlist:
cnffact = NF.cnf(btree) # returns a list of disjunctive clauses
# save any disjunctive clause that is exactly [[RELOP, b1, b2]]:
for clause in cnffact :
if len(clause) == 1 and clause[0][0] in RELOPS :
relop = clause[0][0]
pe1 = PE.evall(C6, clause[0][1])
pe2 = PE.evall(C6, clause[0][2])
if pe1 != {} and pe2 != {} :
newrel = [relop, pe1, pe2]
if newrel not in C6["rels"] :
C6["rels"] = [newrel] + C6["rels"] # new fact at front
#Define sigmoidal activation function and inverse synaptic time constant #~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ fmax=1 v0=1.8 varsigma=0.56 act_fun=ActivationFunction.ActivationFunction(v0,fmax,varsigma) #inverse synaptic time constant zeta=100 #define field initialasation and number of iterations for estimation #~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ mean=[0]*len(Phi) P0=10*pb.eye(len(mean)) x0=pb.multivariate_normal(mean,P0,[1]).T number_of_iterations=10 #ignore first 100 observations allowing the model's initial transients to die out First_n_observations=100 #populate the model NF_model=NF(NF_Connectivity_kernel,sensor_kernel,obs_locns,gamma,gamma_weight,Sigma_varepsilon,act_fun,zeta,Ts,field_space_x_y,spacestep) IDE_model=IDE(IDE_Connectivity_kernel,field,sensor_kernel,obs_locns,gamma,gamma_weight,Sigma_varepsilon,act_fun,x0,P0,zeta,Ts,field_space_x_y,spacestep) #generate Neural Field model NF_model.gen_ssmodel() V,Y=NF_model.simulate(T) #generate the reduced model (state space model) IDE_model.gen_ssmodel() #estimate the states, the connectivity kernel parameters and the synaptic dynamics #~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ps_estimate=para_state_estimation(IDE_model) ps_estimate.itrerative_state_parameter_estimation(Y[First_n_observations:],number_of_iterations)
sensor_center=pb.matrix([[0],[0]]) sensor_width=0.9**2 sensor_kernel=basis(sensor_center,sensor_width,dimension) #Define sigmoidal activation function and inverse synaptic time constant fmax=10 v0=2 varsigma=0.8 act_fun=ActivationFunction(v0,fmax,varsigma) #inverse synaptic time constant zeta=100 #define field initialasation and number of iterations for estimation mean=[0]*len(Phi) P0=10*pb.eye(len(mean)) x0=pb.matrix(pb.multivariate_normal(mean,P0,[1])).T number_of_iterations=10 #ignore first 100 observations allowing the model's initial transients to die out First_n_observations=100 #populate the model NF_model=NF(NF_Connectivity_kernel,sensor_kernel,obs_locns,observation_locs_mm,gamma,gamma_weight,Sigma_varepsilon,act_fun,zeta,Ts,field_space,spacestep) IDE_model=IDE(IDE_Connectivity_kernel,IDE_field,sensor_kernel,obs_locns,gamma,gamma_weight,Sigma_varepsilon,act_fun,x0,P0,zeta,Ts,field_space,spacestep) #generate the Neural Field model NF_model.gen_ssmodel() #V,Y=NF_model.simulate(T) #generate the reduced model (state space model) IDE_model.gen_ssmodel() #estimate the states, the connectivity kernel parameters and the synaptic dynamics #ps_estimate=para_state_estimation(IDE_model) #ps_estimate.itrerative_state_parameter_estimation(Y[First_n_observations:],number_of_iterations)
