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Unit 6: Formalized Symbolic Logics

That conclusion will not need to be derived again when the name server ceases to be the Notes
potential culprit for the problem and we examine instead the routers.

Support Dependency Driven Backtracking

The justification of a sentence, as maintained by the TMS, provides the natural indication of what
assumptions need to be changed if we want to invalidate that sentence.

Our belief [by “our belief” we mean the “inference-engine’s belief”] about a sentence can be:
false, the sentence is believed to be unconditionally false; this is also called a contradiction
true, the sentence is believed unconditionally true; this is also called a premise
assumed-true, the sentence is assumed true [we may change our belief later]; this is also
called an enabled assumption
assumed-false, the sentence is assumed false [we may change our belief later]; this is also
called a retracted assumption

assumed, the sentence is believed by inference from other sentences
don’t-care.
We say if a sentence is true or assumed to be true; it is out of false, assumed-false, or don’t-care.
A TMS maintains a Dependency Network. The network is bipartite, with nodes representing
sentences and justifications. A sentence may correspond to a fact, such as “Socrates is a man”, or
a rule, such as “if ?x is a man then ?x is mortal”. We will say that a sentence node is a premise if
its sentence is true, is a contradiction if its sentence is false, is an assumption if its sentence is
assumed-true or assumed-false or assumed. A sentence node receives arcs from justification
nodes. Each such justification node provides an argument for believing the given sentence node.
In turn, a sentence node has arcs to the justification nodes that use it as a premise. A justification
node has inputs from sentence nodes, its premises or justifiers, and has output to a sentence
node, its conclusion or justification. A justification node represents the inference of the conclusion
from the conjunction of the stated premises. The conventions used in representing graphically
dependency networks are summarized here.
The TMS maintains the following information with each sentence node:

a sentence
a label expressing the current belief in the sentence; it is IN for sentences that are believed,
and OUT for sentences that are not believed.
a list of the justification nodes that support it

a list of the justification nodes supported by it
an indication if the node is an assumption, contradiction, or premise.
The TMS maintains very little information with justification nodes. Only a label with value IN
or OUT depending if we believe the justification valid or not.
The IE can give at least the following orders to the TMS:

create a sentence node with specific properties
create a justification with specific premises and conclusions
attach rules to sentence nodes and execute them when specific beliefs hold at those nodes
[these are like callbacks or triggers; a standard callback informs the IE when a contradiction
becomes true]
retrieve the properties of a sentence node or its justifications and consequences.

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