Institute for Artificial Intelligence
http://hdl.handle.net/10724/19469
2021-01-18T20:11:40ZNatural language plurals in logic programming queries
http://hdl.handle.net/10724/30235
Natural language plurals in logic programming queries
Covington, Michael A.
This paper presents a representation for natural language plurals
in knowledge base queries, implementing collective, distributive, cumulative,
and multiply distributive senses of the plural by means of
higher predicates.
The underlying semantics is based on Franconi’s theory of collections.
The collective reading of a plural applies the predicate to
the whole collection; the distributive reading applies the predicate
to all of the elements; and the cumulative reading says that each element
either satisfies the predicate, or belongs to some collection that
does so. Implicit in the cumulative reading is the notion of element–
property, the property of belonging to some collection that satisfies
a given predicate.
Another reading of the plural, here termed the multiply distributive,
requires a straightforward extension of the system to allow
simultaneous distribution over more than one variable at once,
with none of the distributions having scope over any other. Simultaneous
distribution is implemented as a metalogical predicate that
transforms queries before executing them.
1996-02-01T00:00:00ZToward a new type of language for electronic commerce
http://hdl.handle.net/10724/30233
Toward a new type of language for electronic commerce
Covington, Michael A.
This paper surveys practical issues in the design of a
formal language for business communication (FLBC) in
which transactions are put together by combining meaningful
elements, much as a programming language encodes
algorithms. Such a language is preferable to existing codes
such as ANSI X.12 and UN EDIFACT because of its much
greater versatility. The new language is tentatively named
LEC (Language for Electronic Commerce).
1995-01-01T00:00:00ZNonmonotonic consequence in default model theory
http://hdl.handle.net/10724/30232
Nonmonotonic consequence in default model theory
Zhang, Guo-Qiang; Rounds, William C.
Default model theory is a nonmonotonic formalism for representing and
reasoning about commonsense knowledge. Although this theory is motivated by ideas in
Reiter’s work on default logic, it is a very different, in some sense dual framework. We
make Reiter’s default extension operator into a constructive method of building models,
not theories. Domain theory, which is a well established tool for partial information in the
semantics of programming languages, is adopted as the basis for constructing partial models.
One of the direct advantages of default model theory is that nonmonotonic reasoning can be
conducted with monotonic logics, by using the method of model checking, instead of theorem
proving.
This paper reconsiders some of the laws of nonmonotonic consequence, due to Gabbay
and to Kraus, Lehmann, and Magidor, in the light of default model theory. We remark
that in general, Gabbay’s law of cautious monotony is open to question. We consider an
axiomatization of the nonmonotonic consequence relation omitting this law. We prove a representation
theorem showing that such relations are in one to one correspondence with the
consequence relations determined by extensions in Scott domains augmented with default
sets. This means that defaults are very expressive: they can, in a sense, represent any reasonable
nonmonotonic entailment. Results about what kind of defaults determine cautious
monotony are also discussed. In particular, we show that the property of unique extension
guarantees cautious monotony, and we characterize default structures which determine
unique extensions.
1994-12-07T00:00:00ZLogical considerations on default semantics
http://hdl.handle.net/10724/30230
Logical considerations on default semantics
Rounds, William C.; Zhang, Guo-Qiang
We consider a reinterpretation of the rules of default logic. We make Reiter’s
default rules into a constructive method of building models, not theories. To allow reasoning
in first order systems, we equip standard first-order logic with a (new) Kleene 3-valued
partial model semantics. Then, using our methodology, we add defaults to this semantic
system. The result is that our logic is an ordinary monotonic one, but its semantics is now
nonmonotonic. Reiter’s extensions now appear in the semantics, not in the syntax.
As an application, we show that this semantics gives a partial solution to the conceptual
problems with open defaults pointed out by Lifschitz [16], and Baader and Hollunder [2].
The solution is not complete, chiefly because in making the defaults model-theoretic, we
can only add conjunctive information to our models. This is in contrast to default theories,
where extensions can contain disjunctive formulas, and therefore disjunctive information.
Our proposal to treat the problem of open defaults uses a semantic notion of nonmonotonic
entailment for our logic, deriving from the idea of “only knowing”. Our notion is
“only having information” given by a formula. We discuss the differences between this and
“minimal-knowledge” ideas.
Finally, we consider the Kraus-Lehmann-Magidor [14] axioms for preferential consequence
relations. We find that our consequence relation satisfies the most basic of the laws, and the
Or law, but it does not satisfy the law of Cut, nor the law of Cautious Monotony. We give
intuitive examples using our system, on the other hand, which on the surface seem to violate
these laws, no matter how they are interpreted. We make some comparisons, using our
examples, to probabilistic interpretations for which the laws are true, and we compare our
models to the cumulative models of Kraus, Lehmann, and Magidor. We also show sufficient
conditions for the laws to hold. These involve limiting the use of disjunction in our formulas
in one way or another.
We show how to make use of the theory of complete partially ordered sets, or domain
theory. We can augment any Scott domain with a default set. We state a version of Reiter’s extension operator on arbitrary domains as well. This version makes clear the basic
order-theoretic nature of Reiter’s definitions. A three-variable function is involved. Finding
extensions corresponds to taking fixed points twice, with respect to two of these variables.
In the special case of precondition-free defaults, a general relation on Scott domains induced
from the set of defaults is shown to characterize extensions. We show how a general notion
of domain theory, the logic induced from the Scott topology on a domain, guides us to a
correct notion of “affirmable sentence” in a specific case such as our first-order systems. We
also prove our consequence laws in such a way that they hold not only in first-order systems,
but in any logic derived from the Scott topology on an arbitrary domain.
1994-12-07T00:00:00Z