%Nr: DS-2001-09
%Title: Saying It with Pictures: a Logical Landscape of Conceptual Graphs
%Author: Gwen Kerdiles
Abstract:
Pictorial languages occur in almost every field from roadsigns to
technical design or abstract art.Computer science is no
exception.Understanding the reasons for the uccess of visual
information in human communication and exploiting them in an automated
fashion has gained a prominent place in the artificial intelli- gence
agenda.By considering several aspects of graphical languages in
knowledge representation, this thesis positions conceptual graphs, a
specific diagrammatic framework, at a crossroad of logic, language and
computation.
Some of the cognitive and linguistic efficient features of drawings
play an indisputable role in human and human-machine
communication.Besides these interesting representational tandpoints,
the computational efficiency of reasoning we obtain on some classes of
diagrams emphasises the relevance of pictures in automated reasoning.
In this dissertation, computational complexity is understood in
traditional symbolic terms.As a result, this lays a common ground for
a beneficial interac- tion between usual textual logics and graphical
languages:in the first place, the diagrammatic systems we tudy reveal
the attractive computational complexity of logical fragments that fall
outside the usual paths of symbolic logic.Conversely, some symbolic
characterisations adapt well to the diagrammatic frameworks.For
instance, the notion of guards, which arose from the translation of
modal logics into classical ones, defines a new visual notion of tree
in the conceptual graph paradigm.Moreover, reasoning techniques can be
exchanged between both sides or combined.Finally, cognitive aspects
that are recognised in the perception and manipulation of diagrams
offer new track for expanding established symbolic computational
models with additional visual features.
The central issue of this thesis is to explore these interactions
between con- ceptual graph fragments and symbolic logics, in the light
of standard symbolic complexity models.The main results that are
presented concern graphical proof method for consequence problems and
their complexity analysis in everal con- ceptual graph
languages.Furthermore, by bringing the study into the wider
perspective of visual information in artificial intelligence, we aim
at contributing to the general issue of a better understanding of some
properties of reasoning with diagrams;this appears to be the necessary
basis for further promising connections between symbolic and graphical
perspectives.
The work is organised in five chapters.The first two chapters position
concep- tual graphs in the perspective of everal disciplines involved
in artificial intelli- gence.Chapter 1 relates conceptual graphs to
historical appearances of diagrams in logic, pictorial languages in
knowledge representation, cognitive tudies of vi- sual information and
drawings used in natural language processing.The wide scope of this
overview tresses the relevance of fine-grained studies of visual prop-
erties to the artificial intelligence community as a
whole.Computational logic may be een as common ground for all these
fields when applied to automated reasoning;this is the ubject of the
next chapter.
Chapter 2 presents the technical framework in which the graphical
systems used in the rest of this work will be evaluated.Symbolic
complexity analysis offers fine-structure formal analysis of reasoning
with the graphs and connects the study of visual reasoning to current
interests in expressiveness and complexity in sym- bolic logic.A
geography of complexity results in classical and modal fragments is
then depicted.It ets the scene for the tudy of conceptual graph
languages: several decision problems are relevant and
homomorphism-based method rely on problem equivalence (between model
comparison and consequence)that occur in low-expressive languages.
Chapter 3 introduces the core fragment of imple conceptual graphs and
pro- jection, a consequence calculus based on labelled graph
homomorphism.In ad- dition to the usual semantics of imple graphs,
which is given by a translation to existential conjunctive FOL, a
model-theoretic approach is also provided.It offers a direct handle
for associating projections with model comparisons.By defining a
notion of meta-acyclicity based on guarded quantification and an ap-
propriate projection algorithm, a tractable guarded fragment of imple
graphs is highlighted (Theorem 3.3.7).It includes all previously known
tractable fragments of simple conceptual graphs (i.e.graphs that can
be transformed into equivalent trees).
Chapter 4 explores different possible extensions of the core
language.First, the addition of atomic negation is considered.In the
graph representations, a separation criterion of positive from
negative information defines a fragment of simple graphs with atomic
negation in which projections apply (Theorem 4.1.19). Furthermore, in
the guarded restriction of this fragment, consequence is polyno- mial
(Corollary 4.1.22).Secondly, for a language of conceptual graphs
equivalent to first-order logic, we propose a complete proof method
combining tableau con- struction rules and projections (Chapter
4.2).Finally, in the remaining part of the chapter, a modal
perspective for graph nesting is studied .Reimporting the notion of
guards in this modal framework enables u to define a language of
nested graphs with a tractable associated projection (Corollary
4.3.15).
In the last chapter, we draw our main conclusions from the complexity
results obtained along our chosen route through conceptual graph
landscapes.In partic- ular, the successful interaction of graphical
aspects with symbolic ones suggests promising further paths towards
more visually oriented computation.