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Transcript
The Logic of Existence The Legend of the Unicorn We need to be able to talk about and control the existence and nonexistence of objects and relations Objects can be created or destroyed, but sometimes we need to create objects and relations, then “send them dark” - act as though they do not exist and see what that causes - or evaluate a probability of existence given other information, in the same way we have Bayesian logical values We Use It All The Time The tiger can escape The system shall be capable of... He doubted the existence of a cure He was able to do it It was possible It is commonplace in our everyday language and is a vital part of language modelling Several Forms of Existence • The patient was born without a liver • The liver may stop working at any time • Only consider diseases related to the liver The object may be not present, not functioning or present but not relevant Existence in a Database Cost Cost > 20 Length 10 15 2 6 23 45 44 56 78 23 11 6 A database handles current existence by marking records in or out of a working set - this works when the records are static and independent. It also makes a closed world assumption - no record, doesn’t exist Marking the Structure In a huge active structure, we have to block propagation into areas that are not relevant, by indicating they do not exist for the current analysis Existence needs to be computable and propagatable Orthogonal Properties Existence State Value We need to determine existence before we determine logical state before we determine value - a value on one object may determine existence on another if glycosine_level > 0.3 then Antibody is present Existence Web Does Not Exist Exist Leg Some links only transmit existence, some links transmit the object, its existence and its state - the existence web is interleaved with other webs for logic and objects Types of Existence • Does Exist • May Exist - values 0 - 1.0 • Does Not Exist This matches Bayesian logical values of True/False. The midpoint of the range - 0.5 - has a special significance of DontCare or Ignore. This value can be propagated over the top of existing values when existence is to be ignored. The EXISTS Operator False DoesNotExist EXISTS UKE 0.5 MayExist 0.5 The EXISTS operator links between True/False and DoesExist/DoesNotExist, with Bayesian values on one side represented on the other side by MayExist values Conversion is automatic at logical connectives - AND, OR, IF...THEN etc. Operators Handling Existence A X PLUS If B does not exist, the PLUS operator assumes zero. If B may exist, the operator assumes a range of B,0 The MULTIPLY operator behaves differently, passing along the DoesNotExist B C The Cause Operator Existence Control Mutation Relation Object CAUSE Logical Control Disease This is shorthand for IF Mutation EXISTS AND Other Conditions THEN Disease (an object) EXISTS If Disease is to be ignored, then Mutation will be ignored, and vice versa Relation Operator Fred can cross the bridge The RELATION operator has both logical and existential control linked together in the operator so the logical control cannot have a greater probability than the existence value - here “can” asserts existence, so the logical value can be anything Relation Operator Fred can’t cross the bridge Here we build a structure, then say it does not exist and let it affect whatever it may As a corollary, it must be logically false (within the timeframe of its nonexistence) He Failed … He failed to prevent a riot There is an implication that it was possible for him to prevent a riot, otherwise he would not have failed, he would have been unable to prevent a riot. ToFail puts out a propositional False and an Existential True, so ToPrevent exists. Multiple Causes and Effects Mutation1 A N D CAUSE Mutation2 CAUSE Mutation3 CAUSE Logic operators now handle existence interchangeably with logic - they combine causes and effects around variables. Disease O R Other Causes No Effect - No Existence Mutation1 CAUSE Disease_1 CAUSE Disease_2 A N D If the existence of the object has no effect, then ignore the object. If there were an OtherEffects connection, the inference could not be made. Handling Classes May Exist Gene_1 Genes Does Exist M E M B E R Gene_1 Gene_2 Genes Gene_3 Gene_4 Does Exist Does Not Exist M E M B E R Gene_2 Gene_3 Gene_4 Attributes Controlling Existence Gene_1 Genes ATTRIBUTES Att_1 Att_2 M E M B E R Gene_2 Gene_3 Gene_4 Does Not Exist (In General) Finding Attributes MEMBERS MEMBERS MEMBERS MEMBERS G1 16 “q1.3“ Attributes are found by exciting the structure. Existence can be controlled to vary attributes under different conditions - parts of the structure temporarily cease to exist Dynamically Created Sets • Diseases specific to the liver • Diseases common to liver and kidney • Commonality between chromosomes 10 and 21 These are not really sets, just areas of the structure that are activated into existence, while other areas are either not activated, or activated out of existence - the control structures to do this are generated from the question Activate To Search Other Cause The structure represents everything in the text An existence pulse travels through the structure Extent of Activation Up to now we have been assuming all the structure we have built is to be active, and switching off selected areas using logical control. This method is not effective for huge structures instead, we need to control the area of activation. The huge structures will mostly be about objects, whose existence or nonexistence or irrelevance for current analysis we will need to control Mouldable Search Space Other Cause Knowledge Space Search Space Other Cause You decide what to include and what to ignore, by examining what is currently being ignored Legal Existence Legal text is full of references to existence • Tenant can use the entire Premises • Landlord shall be able to determine • Any Transfer shall, at the option of Landlord, constitute a Default • specific consent from Landlord shall not be required • Under these circumstances, Section 9 is void Structures that represent such text need to be able to modify and control existence from afar - to treat existence as having a value like anything else Logic of Existence The logic of existence handles the existence or nonexistence of objects. It can be freely intermixed with propositional logic, amplifying the efficacy of Bayesian values in the process. Separate control and propagation of existence is necessary to prevent smearing - the confusion between propositional logic and existence logic. Its ability to excite a structure and return information about the connections in it opens up areas of analysis closed to numbers and Boolean logic.