1,638 research outputs found
Blow up and Blur constructions in Algebraic Logic
The idea in the title is to blow up a finite structure, replacing each
'colour or atom' by infinitely many, using blurs to represent the resulting
term algebra, but the blurs are not enough to blur the structure of the finite
structure in the complex algebra. Then, the latter cannot be representable due
to a {finite- infinite} contradiction. This structure can be a finite clique in
a graph or a finite relation algebra or a finite cylindric algebra. This theme
gives examples of weakly representable atom structures that are not strongly
representable. Many constructions existing in the literature are placed in a
rigorous way in such a framework, properly defined.
This is the essence too of construction of Monk like-algebras, one constructs
graphs with finite colouring (finitely many blurs), converging to one with
infinitely many, so that the original algebra is also blurred at the complex
algebra level, and the term algebra is completey representable, yielding a
representation of its completion the complex algebra.
A reverse of this process exists in the literature, it builds algebras with
infinite blurs converging to one with finite blurs. This idea due to Hirsch and
Hodkinson, uses probabilistic methods of Erdos to construct a sequence of
graphs with infinite chromatic number one that is 2 colourable. This
construction, which works for both relation and cylindric algebras, further
shows that the class of strongly representable atom structures is not
elementary.Comment: arXiv admin note: text overlap with arXiv:1304.114
Unifiability and Structural Completeness in Relation Algebras and in Products of Modal Logic S5
Unifiability of terms (and formulas) and structural completeness in the variety of relation algebras RA and in the products of modal logic S5 is investigated. Nonunifiable terms (formulas) which are satisfiable in varieties (in logics) are exhibited. Consequently, RA and products of S5 as well as representable diagonal-free n-dimensional cylindric algebras, RDfn, are almost structurally complete but not structurally complete. In case of S5ⁿ a basis for admissible rules and the form of all passive rules are provided
Deciding regular grammar logics with converse through first-order logic
We provide a simple translation of the satisfiability problem for regular
grammar logics with converse into GF2, which is the intersection of the guarded
fragment and the 2-variable fragment of first-order logic. This translation is
theoretically interesting because it translates modal logics with certain frame
conditions into first-order logic, without explicitly expressing the frame
conditions.
A consequence of the translation is that the general satisfiability problem
for regular grammar logics with converse is in EXPTIME. This extends a previous
result of the first author for grammar logics without converse. Using the same
method, we show how some other modal logics can be naturally translated into
GF2, including nominal tense logics and intuitionistic logic.
In our view, the results in this paper show that the natural first-order
fragment corresponding to regular grammar logics is simply GF2 without extra
machinery such as fixed point-operators.Comment: 34 page
Group decision making and quality-of-information in e-Health systems
Knowledge is central to the modern economy and society. Indeed, the knowledge society has transformed
the concept of knowledge and is more and more aware of the need to overcome the lack of knowledge when has to
make options or address its problems and dilemmas. One`s knowledge is less based on exact facts and more on
hypotheses, perceptions or indications. Even when we use new computational artefacts and novel methodologies for
problem solving, like the use of Group Decision Support Systems (GDSS), the question of incomplete information is
in most of the situations marginalized. On the other hand, common sense tells us that when a decision is made it is
impossible to have a perception of all the information involved and the nature of its intrinsic quality. Therefore,
something has to be made in terms of the information available and the process of its evaluation. It is under this
framework that a Multi-valued Extended Logic Programming language will be used for knowledge representation
and reasoning, leading to a model that embodies the Quality-of-Information (QoI) and its quantification, along the
several stages of the decision making process. In this way it is possible to provide a measure of the value of the QoI
that supports the decision itself. This model will be here presented in the context of a GDSS for VirtualECare, a
system aimed at sustaining online healthcare services
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