3,805 research outputs found
Human inference beyond syllogisms: an approach using external graphical representations.
Research in psychology about reasoning has often been restricted to relatively inexpressive statements involving quantifiers (e.g. syllogisms). This is limited to situations that typically do not arise in practical settings, like ontology engineering. In order to provide an analysis of inference, we focus on reasoning tasks presented in external graphic representations where statements correspond to those involving multiple quantifiers and unary and binary relations. Our experiment measured participants' performance when reasoning with two notations. The first notation used topological constraints to convey information via node-link diagrams (i.e. graphs). The second used topological and spatial constraints to convey information (Euler diagrams with additional graph-like syntax). We found that topo-spatial representations were more effective for inferences than topological representations alone. Reasoning with statements involving multiple quantifiers was harder than reasoning with single quantifiers in topological representations, but not in topo-spatial representations. These findings are compared to those in sentential reasoning tasks
Flow Logic
Flow networks have attracted a lot of research in computer science. Indeed,
many questions in numerous application areas can be reduced to questions about
flow networks. Many of these applications would benefit from a framework in
which one can formally reason about properties of flow networks that go beyond
their maximal flow. We introduce Flow Logics: modal logics that treat flow
functions as explicit first-order objects and enable the specification of rich
properties of flow networks. The syntax of our logic BFL* (Branching Flow
Logic) is similar to the syntax of the temporal logic CTL*, except that atomic
assertions may be flow propositions, like or , for
, which refer to the value of the flow in a vertex, and
that first-order quantification can be applied both to paths and to flow
functions. We present an exhaustive study of the theoretical and practical
aspects of BFL*, as well as extensions and fragments of it. Our extensions
include flow quantifications that range over non-integral flow functions or
over maximal flow functions, path quantification that ranges over paths along
which non-zero flow travels, past operators, and first-order quantification of
flow values. We focus on the model-checking problem and show that it is
PSPACE-complete, as it is for CTL*. Handling of flow quantifiers, however,
increases the complexity in terms of the network to , even
for the LFL and BFL fragments, which are the flow-counterparts of LTL and CTL.
We are still able to point to a useful fragment of BFL* for which the
model-checking problem can be solved in polynomial time. Finally, we introduce
and study the query-checking problem for BFL*, where under-specified BFL*
formulas are used for network exploration
Two-variable Logic with Counting and a Linear Order
We study the finite satisfiability problem for the two-variable fragment of
first-order logic extended with counting quantifiers (C2) and interpreted over
linearly ordered structures. We show that the problem is undecidable in the
case of two linear orders (in the presence of two other binary symbols). In the
case of one linear order it is NEXPTIME-complete, even in the presence of the
successor relation. Surprisingly, the complexity of the problem explodes when
we add one binary symbol more: C2 with one linear order and in the presence of
other binary predicate symbols is equivalent, under elementary reductions, to
the emptiness problem for multicounter automata
Logic Programming Applications: What Are the Abstractions and Implementations?
This article presents an overview of applications of logic programming,
classifying them based on the abstractions and implementations of logic
languages that support the applications. The three key abstractions are join,
recursion, and constraint. Their essential implementations are for-loops, fixed
points, and backtracking, respectively. The corresponding kinds of applications
are database queries, inductive analysis, and combinatorial search,
respectively. We also discuss language extensions and programming paradigms,
summarize example application problems by application areas, and touch on
example systems that support variants of the abstractions with different
implementations
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