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Fig. 3.1
An example semantic network
former champions of logic currently do not believe that human intelligence can be
construed as logical inference, but researchers still actively pursue the field as it is
of crucial importance to many systems, such as those used in mathematical proof-
proving, and it is still used in many less ambitious knowledge-reasoning systems
such as ISO Common Logic (Delugach 2007).
The classical artificial intelligence programme, while fixated on finding a formal
language capable of expressing human knowledge, had ignored the problem of
tractable inference. This problem came to attention abruptly when KRL, one of
the most flexible knowledge representation languages pioneered by Winograd was
found to have intractable inference even on simple problems of cryptarithmetic,
despite its representational richness. 1 Furthermore, while highly optimized infer-
ence mechanisms existed for first-order logic, first-order predicate logic was proven
to be undecidable. These disadvantages of alternative representational formats and
first-order logic led many researchers, particularly those interested in an alternative
“slot and value” knowledge representation language known as frames to begin
researching the decidability of their inference mechanisms (Minsky 1975). This
research into frames then evolved into research on description logics ,where
the trade-offs between the tractability and expressivity were carefully studied
(Levensque and Brachman 1987). The goal of the field was to produce a logic with
decidable inference while maintaining maximum expressivity. Although the first
description-logic system, KL-ONE, was proven to have undecidable inference for
even subsumption, later research produced a vast proliferation of description logics
with carefully categorized decidability and features (Brachman and Schmolze 1985;
Schmidt-Schauss 1989).
1 Personal communication with Henry S. Thompson.
 
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