3,876 research outputs found
Generalising KAT to verify weighted computations
Kleene algebra with tests (KAT) was introduced as an algebraic
structure to model and reason about classic imperative programs, i.e.
sequences of discrete transitions guarded by Boolean tests. This paper
introduces two generalisations of this structure able to express programs
as weighted transitions and tests with outcomes in non necessarily
bivalent truth spaces: graded Kleene algebra with tests (GKAT) and a
variant where tests are also idempotent (I-GKAT). In this context, and
in analogy to Kozen's encoding of Propositional Hoare Logic (PHL) in
KAT we discuss the encoding of a graded PHL in I-GKAT and of its
while-free fragment in GKAT. Moreover, to establish semantics for these
structures four new algebras are de ned: FSET (T ), FREL(K; T )
and FLANG(K; T ) over complete residuated lattices K and T , and
M(n;A) over a GKAT or I-GKAT A. As a nal exercise, the paper
discusses some program equivalence proofs in a graded context.POCI-01-0145-FEDER-03094, NORTE-01-0145-FEDER-000037. ERDF – European Regional Development Fund
through the Operational Programme for Competitiveness and Internationalisation - COMPETE 2020 Programme and by National Funds through the Portuguese funding agency, FCT - Fundação para a Ciência e a Tecnologia, within project POCI-01-0145-FEDER-030947. This paper is also a result of the project SmartEGOV, NORTE-01-0145-FEDER-000037. The second author is supported in the scope of the framework contract foreseen in the numbers 4, 5 and 6 of the article 23, of the Decree-Law 57/2016, of August 29, changed by Portuguese Law 57/2017, of July 19, at CIDMA (Centro de Investigação e Desenvolvimento em Matemática e Aplicações) UID/MAT/04106/2019
Weighted logics for artificial intelligence : an introductory discussion
International audienceBefore presenting the contents of the special issue, we propose a structured introductory overview of a landscape of the weighted logics (in a general sense) that can be found in the Artificial Intelligence literature, highlighting their fundamental differences and their application areas
Fuzzy logic programs as hypergraphs. Termination results
Graph theory has been a useful tool for logic programming in many aspects. In this paper, we propose an equivalent representation of multi-adjoint logic programs using hypergraphs, which are a generalization of classical graphs that allows the use of hypergraph theory in logic programming. Specifically, this representation has been considered in this paper to increase the level and flexibility of different termination results of the computation of the least model of fuzzy logic programs via the immediate consequence operator. Consequently, the least model of more general and versatile fuzzy logic programs can be obtained after finitely many iterations, although infinite programs or programs with loops and general aggregators will be consideredAgencia Estatal de InvestigaciĂłn PID2019-108991GB-I00Junta de AndalucĂa FEDER-UCA18-108612European Union COST Action CA1712
From fuzzy to annotated semantic web languages
The aim of this chapter is to present a detailed, selfcontained and comprehensive account of the state of the art in representing and reasoning with fuzzy knowledge in Semantic Web Languages such as triple languages RDF/RDFS, conceptual languages of the OWL 2 family and rule languages. We further show how one may generalise them to so-called annotation domains, that cover also e.g. temporal and provenance extensions
On kleene algebras for weighted computation
Kleene algebra with tests (KAT) was introduced as an alge-
braic structure to model and reason about classic imperative programs,
i.e. sequences of discrete actions guarded by Boolean tests.
This paper introduces two generalisations of this structure able to ex-
press programs as weighted transitions and tests with outcomes in a not
necessary bivalent truth space, namely graded Kleene algebra with tests
(GKAT) and Heyting Kleene algebra with tests (HKAT).
On these contexts, in analogy to Kozen's encoding of Propositional Hoare
Logic (PHL) in KAT [10], we discuss the encoding of a graded PHL in
HKAT and of its while-free fragment in GKAT.This work is financed by the ERDF - European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation - COMPETE 2020 Programme and by National Funds through the Portuguese funding agency, FCT - Fundacao para a Ciencia e a Tecnologia, within projects POCI-01-0145-FEDER-016692 and UID/MAT/04106/2013. The second author is also supported by the individual grant SFRH/BPD/103004/2014
Logic-Based Decision Support for Strategic Environmental Assessment
Strategic Environmental Assessment is a procedure aimed at introducing
systematic assessment of the environmental effects of plans and programs. This
procedure is based on the so-called coaxial matrices that define dependencies
between plan activities (infrastructures, plants, resource extractions,
buildings, etc.) and positive and negative environmental impacts, and
dependencies between these impacts and environmental receptors. Up to now, this
procedure is manually implemented by environmental experts for checking the
environmental effects of a given plan or program, but it is never applied
during the plan/program construction. A decision support system, based on a
clear logic semantics, would be an invaluable tool not only in assessing a
single, already defined plan, but also during the planning process in order to
produce an optimized, environmentally assessed plan and to study possible
alternative scenarios. We propose two logic-based approaches to the problem,
one based on Constraint Logic Programming and one on Probabilistic Logic
Programming that could be, in the future, conveniently merged to exploit the
advantages of both. We test the proposed approaches on a real energy plan and
we discuss their limitations and advantages.Comment: 17 pages, 1 figure, 26th Int'l. Conference on Logic Programming
(ICLP'10
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