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Now, node (2) and node (5) are IN-nodes, and consequently node (1) and
node (4) are OUT-nodes. Therefore, the contradiction is eliminated.
De Kleer pointed out some limitations of TMS and correspondingly proposed
an assumption-based TMS (ATMS) (de Kleer,1986). A typical characteristic of
ATMS is the capability of working with multiple conreadictory assumptions as
once.
The ATMS consists of two components: a problem solver and a TMS. The
problem solver includes all domain knowledge and inference procedures. Every
inference made is communicated to the TMS. The TMS's job is to determine
what data are believed and disbelieved fiven the justifications records thus far.
An ATMS justification describes how a node is derivable from other nodes,
and is of the following form:
A 1 , A 2 , …, A n ¼ D
Where D is the node being justified and is called the consequent; A 1 , A 2 , …, A n
is a list of nodes and is called the antecedents. The nonlogical notation “ ¼ ” is
used here because the ATMS does not allow negated literals and treats
implication unconventionally.
Limited to the space, detailed discussion of ATMS is omitted here. Readers
may refer to the relevant literatures.
2.10 Situation Calculus
Action is a basic concept in many branches of computer science. For example, in
the branch of database theory, delete, insert and update of data are frequently
used operations (or actions). These operations play an important role in the
database. Another example is the multiagent system of distributed artificial
intelligence, where various behavior (or actions) of agents are the basis of the
cooperation of agents. The knowledge and beliefs of agents is an important
research topic for multiagent system, where the update and revise of knowledge
and beliefs are also based on the study of action theory.
Situation calculus is the most commonly used formalism for the study and
process of actions. With respect to the progress of a database, Fangzhen Lin and
Reiter embed situation calculus into a many-sroted first-order logic framework
LR and established a formal foundation for action (Lin, 1994). In the LR
framework, individuals are divided into three sorts: state, action and object.
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