Case-Based Reasoning Research and Development. Second International
Conference on Case-Based Reasoning, ICCBR-97 Proceedings. Springer-Verlag,
Berlin, Germany; 1997; xiii+648 pp. p.599-610.
Publication Year
1997
Language
English
Abstract
This paper is an attempt at providing a fuzzy set-based formalization
of case-based reasoning. The proposed approach, which does not take into
account the learning aspects of case-based reasoning, assumes the principle
that "the more similar are the problem description attributes, the
more similar are the outcome attributes". A weaker form of this principle
is also considered. These two forms of the case-based reasoning principle
are modelled in terms of fuzzy rules. Then an approximate reasoning machinery
taking advantage of this principle enables us to apply the information
stored in the memory of precedent cases to the current problem. A particular
instance of case-based reasoning, named case-based decision, is especially
investigated. A logical model of case-based inference is also described.
The aim of the paper is to propose dynamic logic as a common logical
framework to describe and identify the most relevant formal characteristics
of multi language logical architectures (MLA) in order to investigate the
expressive power of the knowledge bases that can be built upon them. In
general, a MLA allows to build knowledge bases as a set of units with initial
local theories written in possible different logical languages. Each unit
is also usually allowed to have its own intra unit deductive system. Moreover,
the whole knowledge base is equipped with an additional set of deductive
rules, called bridge rules, to control the information flow among the different
units of the knowledge base. The set of bridge rules act as an inter unit
deductive system. The reasoning dynamics of a knowledge base on top of
a MLA can therefore be described by how the local theories of the units
evolve during execution.
Record
4 of 29
Title
Fuzzy logic and probability
Author
Hajek-P; Godo-L; Esteva-F
Source
Uncertainty in Artificial Intelligence.Proceedings of the Eleventh
Conference (1995). Morgan Kaufmann Publishers, San Francisco, CA, USA;
1995; viii+591 pp. p.237-44.
Publication Year
1995
Language
English
Abstract
In this paper we deal with a new approach to probabilistic reasoning
in a logical framework. Nearly almost all logics of probability that have
been proposed in the literature are based on classical two-valued logic.
After making clear the differences between fuzzy logic and probability
theory, we propose a fuzzy logic of probability for which completeness
results (in a probabilistic sense) are provided. The main idea behind this
approach is that probability values of crisp propositions can be understood
as truth values of some suitable fuzzy propositions associated to the crisp
ones. Moreover, suggestions and examples of how to extend the formalism
to cope with conditional probabilities and with other uncertainty formalisms
are also provided.
Record
5 of 29
Title
On modal logics for qualitative possibility in a fuzzy setting
Author
Hajek-P; Harmancova-D; Esteva-F; Garcia-P; Godo-L
Source
Uncertainty in Artificial Intelligence.Proceedings of the Tenth Conference
(1994). Morgan Kaufmann Publishers, San Francisco, CA, USA; 1994; vi+616
pp. p.278-85.
Publication Year
1994
Language
English
Abstract
Within the possibilistic approach to uncertainty modeling, the paper
presents a modal logical system to reason about qualitative (comparative)
statements of the possibility (and necessity) of fuzzy propositions. We
relate this qualitative modal logic to the many valued analogues MVS5 and
MVKD45 of the well known modal logics of knowledge and belief S5 and KD45
respectively. Completeness results are obtained for such logics and therefore,
they extend previous existing results for qualitative possibilistic logics
in the classical non fuzzy setting.
Record
6 of 29
Title
Similarity-based consequence relations
Author
Dubois-D; Esteva-F; Garcia-P; Godo-L; Prade-H
Source
Symbolic and Quantitative Approaches to Reasoning and Uncertainty.European
Conference, ECSQARU '95. Proceedings. Springer-Verlag, Berlin, Germany;
1995; x+430 pp. p.171-9.
Publication Year
1995
Language
English
Abstract
This paper offers a preliminary investigation of consequence relations
which make sense in a logic of graded similarity, and their application
to interpolative reasoning.
Record
7 of 29
Title
Many-valued epistemic states. An application to a reflective architecture:
Milord-II
Author
Godo-L; van-der-Hoek-W; Meyer-J-JC; Sierra-C
Source
Advances in Intelligent Computing - IPMU '94. 5th International Conference
on Information Processing and Management of Uncertainty in Knowledge-Based
Systems. Springer-Verlag, Berlin, Germany; 1995; xii+628 pp. p.440-52.
Publication Year
1995
Language
English
Abstract
Halpern and Moses (1984) theory on epistemic states and minimizing
knowledge is a formalism with which one can infer what is known and, more
importantly, what is unknown by an agent. This formalism has been used
up to now in a classical two-valued framework. In this paper we formulate
an extension of it when the underlying logic is many-valued, in order to
deal with knowledge possibly pervaded with fuzziness. Then we apply this
extension to the meta-level architecture MILORD II. The object level is
an approximate reasoning component based on many-valued logics. The meta-level
component makes use of some special meta-predicates to reason about the
different states of knowledge of the object level. Our generalization of
Halpern and Moses' theory allows us to interpret meta-level reasoning in
terms of many-valued epistemic states, providing in turn a modal interpretation
of MILORD II meta-predicates.
Record
8 of 29
Title
Query-answering in fuzzy temporal constraint networks
Author
Vila-L; Godo-L
Source
Proceedings of 1995 IEEE International Conference on Fuzzy Systems.The
International Joint Conference of the Fourth IEEE International Conference
on Fuzzy Systems and The Second International Fuzzy Engineering Symposium
(Cat. No.95CH35741). IEEE, New York, NY, USA; 1995; 5 vol. (xxxiv+2342+vii+106)
pp. p.43-8 vol.1.
Publication Year
1995
Language
English
Abstract
Temporal constraint networks are a well-known powerful formalism for
encoding temporal knowledge based on the CSP techniques. A redefinition
of metric temporal constraints to cope with vagueness of temporal relations
based on fuzzy sets, called fuzzy temporal constraint networks has been
proposed previously. In this paper the authors identify those queries on
a fuzzy temporal constraint network relevant to a knowledge-based reasoning
system. The authors provide definitions for their answering and explore
the functions on which they are based by discussing the different choices
for them. These results can be useful to those interested in defining a
system for temporal reasoning under uncertainty. For instance, the authors
satisfactorily applied them to the definition of a possibilistic temporal
reasoning system.
Record
9 of 29
Title
On similarity logic and the generalized modus ponens
Author
Esteva-F; Garcia-P; Godo-L; Ruspini-E; Valverde-L
Source
Proceedings of the Third IEEE Conference on Fuzzy Systems.IEEE World
Congress on Computational Intelligence (Cat. No.94CH3430-6). IEEE, New
York, NY, USA; 1994; 3 vol. (xxxiv+xxvi+xxvii+2118) pp. p.1423-7 vol.2.
Publication Year
1994
Language
English
Abstract
We present an improvement of the similarity-logic interpretation of
the generalized modus ponens rule. The main feature of this new interpretation
is its ability to distinguish between the bodies of evidence corresponding
to antecedent and conditional distributions. Furthermore, we show that
this characterization is consistent with the variable-oriented, fuzzy-logic
concept of generalized modus ponens.
Record
10 of 29
Title
Local multi-valued logics in modular expert systems
We describe an approach to the problem of dealing with uncertainty
by means of finite multi-valued logics in modular expert systems, and the
results obtained. The modularity of the systems allows us to address two
main characteristics of human problem-solving: the adaptation of general
knowledge to particular problems and the dependency of the management of
uncertainty on the different subtasks being implemented in the modules
of the system, i.e. different modules can have different local multiple-valued
logics as part of their local deductive mechanisms. Although the results
obtained are general, we use, throughout the paper, examples of a medical
expert system that has been designed using a modular language called MILORD-II,
that implements them showing the practical interest of the theoretical
concepts involved.
Record
11 of 29
Title
Relating and extending semantical approaches to possibilistic reasoning
Author
Esteva-F; Garcia-Calves-P; Godo-L
Source
International-Journal-of-Approximate-Reasoning.vol.10, no.4; May 1994;
p.311-44.
Publication Year
1994
Language
English
Abstract
Two main semantical approaches to possibilistic reasoning with classical
propositions have been proposed in the literature. Namely, Dubois-Prade's
approach (D. Dubois, H. Prade, 1988) known as possibilistic logic, whose
semantics is based on a preference ordering in the set of possible worlds,
and Ruspini's approach (E.H. Ruspini, 1991) that we redefine and call similarity
logic, which relies on the notion of similarity or resemblance between
worlds. We put into relation both approaches, and it is shown that the
monotonic fragment of possibilistic logic can be semantically embedded
into similarity logic. Furthermore, to extend possibilistic reasoning to
deal with fuzzy propositions, a semantical reasoning framework, called
fuzzy truth-valued logic is also introduced and proved to capture the semantics
of both possibilistic and similarity logics.
Record
12 of 29
Title
From fuzzy logic to fuzzy truth-valued logic for expert systems: a
survey
Author
de-Mantaras-RL; Godo-L
Source
Second IEEE International Conference on Fuzzy Systems (Cat.No.93CH3136-9).
IEEE, New York, NY, USA; 1993; 2 vol. (xviii+xx+1430) pp. p.750-5 vol.2.
Publication Year
1993
Language
English
Abstract
Fuzzy logic is a logic both of vagueness and of incomplete information
in the sense that truth-values can be ill-known and therefore represented
by fuzzy subsets of the unit interval, that is, fuzzy truth-values. Truth
is not an absolute concept. Fuzzy logic provides a way to represent degrees
of certainty. The authors present a comprehensive survey showing that the
fuzzy truth-valued approach has the advantage of being independent of the
particular possibility distributions associated with the condition and
action parts of the rules. An example of reasoning with fuzzy truth-values
is given.
Record
13 of 29
Title
On the relationship between preference and similarity-based approaches
to possibilistic reasoning
Author
Esteva-F; Garcia-Calves-P; Godo-L
Source
Second IEEE International Conference on Fuzzy Systems (Cat.No.93CH3136-9).
IEEE, New York, NY, USA; 1993; 2 vol. (xviii+xx+1430) pp. p.918-23 vol.2.
Publication Year
1993
Language
English
Abstract
Two main approaches to possibilistic reasoning with classical propositions
have been proposed in the literature. The Dubois-Prade approach has a semantics
based on a preference ordering in the set of possible worlds, whereas the
semantics of Ruspini's approach relies on the notion of similarity or resemblance
between worlds. The basic notions of both approaches are presented. The
correspondence between the two approaches is studied. It is shown that
there exists a strong relationship between them. It is demonstrated that
both approaches can be considered as particular cases of a more general
framework of fuzzy reasoning that allows dealing with vague propositions.
Record
14 of 29
Title
Modularity, uncertainty and reflection in MILORD II
Author
Sierra-C; Godo-L
Source
1992 IEEE International Conference on Systems, Man and Cybernetics
(Cat.No.92CH3176-5). IEEE, New York, NY, USA; 1992; 2 vol. xviii+1735 pp.
p.255-60 vol.1.
Publication Year
1992
Language
English
Abstract
Knowledge-based (KB) systems, when programmed in the large, require
special architectures, adapted to implement complex reasoning tasks and
able to combine simple tasks into more sophisticated ones in a safe way.
To tackle this problem MILORD II proposes three basic programming techniques:
modularization, reflection, and local uncertainty management. Modularization
is a technique used to map the task/subtask structure of a problem into
a structured KB. Modules consist of a clean interface, a propositional
object-level language, and a first-order meta-level language. Uncertainty
is managed by means of finite multiple-valued local logics associated to
the object-level language of each module. Reflection between the object-level
and the meta-level languages makes it possible to implement, inside each
module, nonstandard reasoning patterns such as default reasoning or hypothetical
reasoning. The combination of several modules into a structured KB is the
way MILORD II implements complex reasoning patterns.
Record
15 of 29
Title
A specialisation calculus to improve expert systems communication
Author
Puyol-Gruart-J; Godo-L; Sierra-C
Source
ECAI 92.10th European Conference on Artificial Intelligence Proceedings.
Wiley, Chichester, UK; 1992; xviii+876 pp. p.144-8.
Publication Year
1992
Language
English
Abstract
The motivation of the work presented is the improvement of the classical
input/output expert systems behaviour. In an uncertain reasoning context
this behaviour consists of just getting certainty values for propositions.
Instead, the answer of an expert system will be a set of formulas: a set
of propositions and a set of specialised rules containing unknown propositions
in their left part. This type of behaviour is much more informative than
the classical one because it gives to users not only the answer to a query
but all the relevant information to improve the solution. A family of propositional
rule-based languages founded on multiple-valued logics is presented and
formalised. The deductive system defined on top of it is based on a specialisation
inference rule (SIR). The soundness and literal completeness of the deductive
system are proved.
Record
16 of 29
Title
DRUMS: defeasible reasoning and uncertainty management systems
AI-Communications.vol.6, no.1; March 1993; p.27-46.
Publication Year
1993
Language
English
Abstract
The activities are reported of the Basic Research Action 3085 called
DRUMS. This 2.5 year large scale European research project studied several
aspects of uncertainty in artificial intelligence. It has been supported
by a grant from the Commission of the European Communities, ESPRIT II program.
It regrouped 8 university laboratories, 3 research institutions and 3 industrial
research centers. It might be of interest to the AI community to be informed
of the activities and achievements of this large European research consortium
(even if this group represents only a limited subset of the European researchers
working in this areas). This information might help in creating larger
international collaborations and permits to those interested to contact
the DRUMS consortium.
IEEE International Conference on Fuzzy Systems (Cat.No.92CH3073-4).
IEEE, New York, NY, USA; 1992; xxii+1438 pp. p.787-94.
Publication Year
1992
Language
English
Abstract
MILORD is a working expert system shell oriented to classification
tasks. The authors describe a modular extension of the MILORD system. This
modular extension, called MILORD-II, addresses two main characteristics
of human problem solving: the application of general knowledge to particular
problems, and the dependence of the kind of management of uncertainty on
the particular subtasks. The focus is on the two important roles uncertainty
plays in this modular system: (i) as part of local deductive mechanisms,
and (ii) as a control feature in the process of selecting and combining
knowledge base units or modules.
Record
18 of 29
Title
Entailment and inference in fuzzy logic using fuzzy preorders
Author
Godo-L; Valverde-L
Source
IEEE International Conference on Fuzzy Systems (Cat.No.92CH3073-4).
IEEE, New York, NY, USA; 1992; xxii+1438 pp. p.587-94.
Publication Year
1992
Language
English
Abstract
Within the framework of fuzzy logic, the notion of semantic entailment
and its relationship with inference is analysed. In particular, the case
of conditional statements modeled through fuzzy preorders is considered.
The main results exhibit a strong relationship between the notions of entailment
and implication, driven by the pointwise order of the unit interval In
the case of R-implications, and by suitable modifications of this order,
in the case of general fuzzy preorders.
Record
19 of 29
Title
Linguistically expressed uncertainty; its elicitation and use in modular
expert systems
Author
Godo-L; Lopez-de-Mantaras-R
Source
Symbolic and Quantitative Approaches to Uncertainty.European Conference
ECSQAU. Proceedings. Springer-Verlag, Berlin, Germany; 1991; xi+362 pp.
p.76-80.
Publication Year
1991
Language
English
Abstract
The paper describes the work performed in the ESPRIT Basic Research
Action DRUMS, on the elicitation and use of finite sets of linguistic expressions
of uncertainty within modular expert systems. Such finite sets of linguistic
terms, together with their connective operators define multiple-valued
local logics associated with different modules implementing different subtasks
of the expert system Taking this into account, the authors aim is twofold:
first, to provide a general logical framework in order to be able to work
simultaneously with several local multiple-valued logics, and second, to
develop a software tool to help in the process of the elicitation of the
linguistic expressions and of the connective operators within these local
logics.
Record
20 of 29
Title
MILORD: the architecture and the management of linguistically expressed
uncertainty
Describes the MILORD Shell and particularly its architecture and its
management of uncertainty. MILORD is an expert systems building tool consisting
of two inference engines and an explanation module. The system allows one
to perform different calculi of uncertainty on an expert defined set of
linguistic terms expressing uncertainty. The different calculi of uncertainty
applied to the set of linguistic terms give, as a result, a fuzzy subset
that is approximated, by means of a linguistic approximation process, to
a linguistic certainty value belonging to the set of linguistic terms.
This linguistic approximation keeps the calculus of uncertainty closed.
This has the advantage that, once the linguistic certainty values have
been defined, the system computes, offline, the conjunction, disjunction
and implication operations for all the pairs of linguistic uncertainty
values in the term set and stores the results in matrices. Therefore, when
MILORD is run, the propagation and combination of uncertainty is performed
by simply accessing these precomputed matrices. MILORD also deals with
nonmonotonic reasoning in the same framework of uncertainty management.
Finally, an application to the diagnosis and treatment of pneumonia is
presented.
Record
21 of 29
Title
Fuzzy values in fuzzy logic
Author
Godo-L; Jacas-J; Valverde-L
Source
International-Journal-of-Intelligent-Systems.vol.6, no.2; March 1991;
p.199-212.
Publication Year
1991
Language
English
Abstract
One of the main features of fuzzy logic is its capability to deal with
the concept of compatibility between two propositions, in such a way that
the inference process modeled through the compositional rule of inference
is independent from the particular possibility distributions involved.
It is in this context that the compatibility functions can be considered
as fuzzy truth values, labels or qualifications, playing the same role
as the values true and false play in the classical logic, where the meaning
of propositions is nothing but its truth value. The authors consider a
restricted family of labels having the following desirable properties:
(a) easy parametric representation, (b) easy semantic interpretation, (c)
to allow a gradation in the family according to the modifications performed
by each label, and (d) to be closed under inference processes (FR-functions),
and also under some suitable and meaningful operations between them.
Record
22 of 29
Title
A formal semantical approach to fuzzy logic
Author
Godo-L; Esteva-F; Garcia-P; Agusti-Cullell-J
Source
Proceedings of the Twenty-First International Symposium on Multiple-Valued
Logic (Cat. No.91CH3009-8). IEEE Comput. Soc. Press, Los Alamitos, CA,
USA; 1991; xi+383 pp. p.72-9.
Publication Year
1991
Language
English
Abstract
A formal semantical approach to fuzzy logic is given, formalizing it
as a family of institutions. In this frame the soundness of the most-used
inference patterns in fuzzy logic is proved. The authors believe that this
formalization of fuzzy logic can be used to prove the soundness of other
inference patterns such as the principle of resolution or the chaining
inference rule.
Record
23 of 29
Title
Formalizing multiple-valued logics as institutions
Author
Agusti-Cullell-J; Esteva-F; Garcia-P; Godo-L
Source
Uncertainty in Knowledge Bases.3rd International Conference on Information
Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU
'90. Springer-Verlag, Berlin, Germany; 1991; x+609 pp. p.269-78.
Publication Year
1991
Language
English
Abstract
Many of the uncertainty management systems used in knowledge-based
systems technology can be considered as the set of mechanisms that a certain
underlying multiple-valued logic supplies; certainty values, numeric or
linguistic, would be the truth-values of that logic, a knowledge base would
be a set of axioms, and the mechanisms of uncertainty combination and propagation
would be the inference rules of the deduction system. The authors formalize
multiple-valued logics inside the institutional framework. They structure
multiple-valued logics as families of institutions, each one being indexed
by a class of truth-values algebras, in such a way that each morphism between
truth-values algebras determines a corresponding morphism of institutions.
These institution morphisms are a basic mechanism in modular expert system
languages in order to build uncertainty management systems that deal with
different logics in different modules.
Record
24 of 29
Title
VLSI chip-architecture selection using reasoning based on fuzzy logic
Author
Felix-R; Hoffmann-A; Moraga-C; Godo-L; Sierra-C
Source
Proceedings.The Nineteenth International Symposium on Multiple-Valued
Logic (Cat. No.89CH2751-6). IEEE Comput. Soc. Press, Washington, DC, USA;
1989; xv+464 pp. p.165-71.
Publication Year
1989
Language
English
Abstract
A knowledge-based system is presented which carries out a design step
in very large-scale integration (VLSI) chip synthesis, namely, VLSI chip-architecture
selection. The system decides which VLSI chip-architecture scheme (i.e.
a general architectural principle representing a class of chip architectures)
best fits a list of architectural properties given as input to the system.
However, the input information is usually uncertain and/or incomplete.
The system models chip-architecture selection using a reasoning mechanism
based on fuzzy logic.
Record
25 of 29
Title
A new approach to connective generation in the framework of expert
systems using fuzzy logic
Author
Godo-L; Sierra-C
Source
Proceedings of the Eighteenth International Symposium on Multiple-Valued
Logic (Cat. No.88CH2546-0). IEEE Comput. Soc. Press, Washington, DC, USA;
1988; xiii+422 pp. p.157-62.
Publication Year
1988
Language
English
Abstract
A technique for modeling uncertainty in expert systems is presented.
Operators are defined using linguistic terms to avoid any numerical representation.
These operators consider linguistic term set ordering, constraints that
are the counterpart of properties fulfilled by triangular norms in fuzzy
logic, and additional restrictions created by the expert's procedure to
combining certainty. The method avoids the usual problems that arise in
other treatments of certainty linguistic terms, where they are represented
as fuzzy numbers or fuzzy truth labels. One of the most significant problems
is the lack of consensus in the representation of each term by a group
of experts, due to the necessity of representing the terms in a pseudonumerical
scale.
Record
26 of 29
Title
Possibilistic temporal reasoning based on fuzzy temporal constraints
Author
Godo-L; Vila-L
Source
IJCAI-95.Proceedings of the Fourteenth International Joint Conference
on Artificial Intelligence. Morgan Kaufmann Publishers, San Mateo, CA,
USA; 1995; 2 vol. (xxx+xiii+2077) pp. p.1916-22 vol.2.
Publication Year
1995
Language
English
Abstract
In this paper we propose a propositional temporal language based on
fuzzy temporal constraints which turns out to be expressive enough for
domains-like many coming from medicine-where knowledge is of propositional
nature and an explicit handling of time, imprecision and uncertainty are
required. The language is provided with a natural possibilistic semantics
to account for the uncertainty issued by the fuzziness of temporal constraints.
We also present an inference system based on specific rules dealing with
the temporal constraints and a general fuzzy modus ponens rule whereby
behaviour is shown to be sound. The analysis of the different choices as
fuzzy operators leads us to identify the well-known Lukasiewicz implication
as very appropriate to define the notion of possibilistic entailment, an
essential element of our inference system.
Record
27 of 29
Title
From intervals to fuzzy truth-values: Adding flexibility to reasoning
under uncertainty
Author
Lopez-De-Mantaras-R; Godo-L
Source
International-Journal-of-Uncertainty,-Fuzziness-and-Knowledge-Based-Systems.vol.5,
no.3; June 1997; p.251-60.
Publication Year
1997
Language
English
Abstract
In dealing with representing knowledge under uncertainty there is a
sustained tendency to increase flexibility in order to avoid problems of
inconsistency in the knowledge. Early uncertainty management systems dealt
with single real values within a predefined range, soon interval valued
approaches were proposed and more recently we have witnessed the introduction
of fuzzy-interval valued approaches, i.e., possibility distributions and
fuzzy truth-values. In this paper we describe these fuzzy set based approaches
with an emphasis on the concept of fuzzy truth-value.
Record
28 of 29 in INSPEC 1/97-6/97
Title
A logical approach to interpolation based on similarity relations
Author
Dubois-D; Prade-H; Esteva-F; Garcia-P; Godo-L
Source
International-Journal-of-Approximate-Reasoning.vol.17, no.1; July 1997;
p.1-36.
Publication Year
1997
Language
English
Abstract
One of the possible semantics of fuzzy sets is in terms of similarity;
namely, a grade of membership of an item in a fuzzy set can be viewed as
the degree of resemblance between this item and prototypes of the fuzzy
set. In such a framework, an interesting question is how to devise a logic
of similarity, where inference rules can account for the proximity between
interpretations. The aim is to capture the notion of interpolation inside
a logical setting. The authors investigate how a logic of similarity dedicated
to interpolation can be defined by considering different natural consequence
relations induced by the presence of a similarity relation on the set of
interpretations. These consequence relations are automatically characterized
in a way that parallels the characterization of nonmonotonic consequence
relationships. It is shown how to reconstruct the similarity relation underlying
a given family of consequence relations that obey the axioms. Their approach
strikingly differs from the logics of indiscernibility, such as the rough-set
logics, because emphasis is put on interpolation capabilities. Potential
applications are fuzzy rule-based systems and fuzzy case-based reasoning,
where notions of similarity play a crucial role.
One of the goals of a variety of approximate reasoning models is to
cope with inference patterns more flexible than those of classical reasoning.
Among them, similarity-based reasoning aims at modeling notions of resemblance
or proximity among propositions and consequence relations which make sense
in such a setting. One way of proceeding is to equip the set of interpretations
or possible worlds with a similarity relation S, that is, a reflexive,
symmetric and t-norm-transitive fuzzy relation. The authors explore a modal
approach to similarity-based reasoning and define three multimodal systems
with similarity-based Kripke model semantics. A similarity-based Kripke
model is a structure <W,S,|| ||>, in which W is the set of possible
worlds, || || represents an assignment of possible worlds to atomic formulas,
and S is a similarity function S:W*W to G, where G is a subset of the unit
interval [0,1] such that 0,1 in G. They provide soundness and completeness
results for these systems with respect to some classes of the above structures.