Abstract : This report is devoted to a theoretical analysis of inheritance in monotonic semantic nets with positive and negative links, but without relations. We establish several basic results. After setting out the fundamental ideas behind monotonic inheritance, we characterize the inheritance relation through a sequent calculus, or natural-deduction system, that is relatively natural and well-motivated. It is often thought that the logic of monotonic semantic nets, at least, is simply the classical predicate calculus. We show that this is not so. The logic we present is non-classical, and it is proved to be both sound and complete with respect to monotonic inheritance relation is also equivalent to a notion of validity arising from interpretations over a certain four-valued matrix that has been thought to have some computational significance. One traditional attraction of inheritance networks has always been their natural correspondence with graphs, which makes them particularly appropriate as vehicles of knowledge representation for concurrent computing architectures, where graph-searches can be very fast. The last section we present inference algorithms over monotonic semantic nets for such a concurrent architecture, the Parallel Marker Propagation Machine defined by Scott Fahlman. The algorithms are proved to be correct and complete.
[1]
C. Driver.
The relevance of relevance
,
1976
.
[2]
Bas C. van Fraassen,et al.
Quantification as an act of mind
,
1982,
J. Philos. Log..
[3]
Brian Ellis,et al.
Rational Belief Systems.
,
1980
.
[4]
Martha Kneale,et al.
The development of logic
,
1963
.
[5]
Nuel D. Belnap,et al.
A Useful Four-Valued Logic
,
1977
.
[6]
Timothy Smiley,et al.
What is a syllogism?
,
1973,
J. Philos. Log..
[7]
John C. Mitchell,et al.
Realisability Semantics for Error-Tolerant Logics
,
1986,
TARK.
[8]
Hugues Leblanc,et al.
Alternatives to Standard First-Order Semantics
,
1989
.
[9]
John Corcoran,et al.
Aristotle’s Natural Deduction System
,
1974
.
[10]
Nuel D. Belnap,et al.
How a Computer Should Think
,
2019,
New Essays on Belnap-Dunn Logic.
[11]
Stuart C. Shapiro,et al.
Theoretical Foundations for Belief Revision
,
1986,
TARK.
[12]
Scott E. Fahlman,et al.
NETL: A System for Representing and Using Real-World Knowledge
,
1979,
CL.
[13]
W. Daniel Hillis,et al.
The connection machine
,
1985
.
[14]
John Corcoran,et al.
Ancient Logic and its Modern Interpretations
,
1974
.
[15]
P. Hayes.
The Logic of Frames
,
1981
.
[16]
David S. Touretzky,et al.
The Mathematics of Inheritance Systems
,
1984
.