165 research outputs found
On the generation of equational dynamic logics for weighted imperative programs
Dynamic logic is a powerful framework for reasoning about
imperative programs. This paper extends previous work [9] on the systematic
generation of dynamic logics from the propositional to the equational
case, to capture `full-
edged' imperative programs. The generation
process is parametric on a structure specifying a notion of `weight' assigned
to programs. The paper introduces also a notion of bisimilarity
on models of the generated logics, which is shown to entail modal equivalence
with respect to the latter.POCI-01-0145-FEDER-030947. 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. 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 and by UID/MAT/04106/2019 at CIDM
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
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
A family of graded epistemic logics
Multi-Agent Epistemic Logic has been investigated in Computer Science [5] to represent and reason about
agents or groups of agents knowledge and beliefs. Some extensions aimed to reasoning about knowledge
and probabilities [4] and also with a fuzzy semantics have been proposed [6,13].
This paper introduces a parametric method to build graded epistemic logics inspired in the systematic
method to build Multi-valued Dynamic Logics introduced in [11,12]. The parameter in both methods is the
same: an action lattice [9]. This algebraic structure supports a generic space of agent knowledge operators,
as choice, composition and closure (as a Kleene algebra), but also a proper truth space for possible non
bivalent interpretation of the assertions (as a residuated lattice)
A family of graded epistemic logics
Multi-Agent Epistemic Logic has been investigated in Computer Science [5] to represent and reason about
agents or groups of agents knowledge and beliefs. Some extensions aimed to reasoning about knowledge
and probabilities [4] and also with a fuzzy semantics have been proposed [6,13].
This paper introduces a parametric method to build graded epistemic logics inspired in the systematic
method to build Multi-valued Dynamic Logics introduced in [11,12]. The parameter in both methods is the
same: an action lattice [9]. This algebraic structure supports a generic space of agent knowledge operators,
as choice, composition and closure (as a Kleene algebra), but also a proper truth space for possible non
bivalent interpretation of the assertions (as a residuated lattice)
Probabilistic data flow analysis: a linear equational approach
Speculative optimisation relies on the estimation of the probabilities that
certain properties of the control flow are fulfilled. Concrete or estimated
branch probabilities can be used for searching and constructing advantageous
speculative and bookkeeping transformations.
We present a probabilistic extension of the classical equational approach to
data-flow analysis that can be used to this purpose. More precisely, we show
how the probabilistic information introduced in a control flow graph by branch
prediction can be used to extract a system of linear equations from a program
and present a method for calculating correct (numerical) solutions.Comment: In Proceedings GandALF 2013, arXiv:1307.416
A family of graded epistemic logics
Multi-Agent Epistemic Logic has been investigated in Computer Science [Fagin, R., J. Halpern, Y. Moses and M. Vardi, “Reasoning about Knowledge,” MIT Press, USA, 1995] to represent and reason about agents or groups of agents knowledge and beliefs. Some extensions aimed to reasoning about knowledge and probabilities [Fagin, R. and J. Halpern, Reasoning about knowledge and probability, Journal of the ACM 41 (1994), pp. 340–367] and also with a fuzzy semantics have been proposed [Fitting, M., Many-valued modal logics, Fundam. Inform. 15 (1991), pp. 235–254; Maruyama, Y., Reasoning about fuzzy belief and common belief: With emphasis on incomparable beliefs, in: IJCAI 2011, Proceedings of the 22nd International Joint Conference on Artificial Intelligence, Barcelona, Catalonia, Spain, July 16–22, 2011, 2011, pp. 1008–1013]. This paper introduces a parametric method to build graded epistemic logics inspired in the systematic method to build Multi-valued Dynamic Logics introduced in [Madeira, A., R. Neves and M. A. Martins, An exercise on the generation of many-valued dynamic logics, J. Log. Algebr. Meth. Program. 85 (2016), pp. 1011–1037. URL http://dx.doi.org/10.1016/j.jlamp.2016.03.004; Madeira, A., R. Neves, M. A. Martins and L. S. Barbosa, A dynamic logic for every season, in: C. Braga and N. Martí-Oliet, editors, Formal Methods: Foundations and Applications – 17th Brazilian Symposium, SBMF 2014, Maceió, AL, Brazil, September 29-October 1, 2014. Proceedings, Lecture Notes in Computer Science 8941 (2014), pp. 130–145. URL http://dx.doi.org/10.1007/978-3-319-15075-8_9]. The parameter in both methods is the same: an action lattice [Kozen, D., On action algebras, Logic and Information Flow (1994), pp. 78–88]. This algebraic structure supports a generic space of agent knowledge operators, as choice, composition and closure (as a Kleene algebra), but also a proper truth space for possible non bivalent interpretation of the assertions (as a residuated lattice).publishe
An exercise on the generation of many-valued dynamic logics
In the last decades, dynamic logics have been used in different domains as a suitable
formalism to reason about and specify a wide range of systems. On the other hand,
logics with many-valued semantics are emerging as an interesting tool to handle devices
and scenarios where uncertainty is a prime concern. This paper contributes towards the
combination of these two aspects through the development of a method for the systematic
construction of many-valued dynamic logics. Technically, the method is parameterised
by an action lattice that defines both the computational paradigm and the truth space
(corresponding to the underlying Kleene algebra and residuated lattices, respectively)
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