In this paper we propose the use of a set of weights in fuzzy modelling, the class weights, which are assigned to each class of a classification problem. We automatically generate a fuzzy model, using a three-stage methodology: (i) generation of a crisp model from a decision tree, induced from the data, (ii) transformation of the crisp model into a fuzzy one, and (iii) optimization of the fuzzy...

In this paper we propose a complete axiomatization of the bisimilarity distance of Desharnais et al. for the class of finite labelled Markov chains. Our axiomatization is given in the style of a quantitative extension of equational logic recently proposed by Mardare, Panangaden, and Plotkin (LICS 2016) that uses equality relations t ≡ε s indexed by rationals, expressing that “t is approximately...

We present a novel approach based on inductive theorem proving for verifying invariants of dynamic systems specified in rewriting logic, a formal specification language implemented in the Maude system. An invariant is a property that holds on all the states that are reachable from a given class of initial states. Our approach consists in encoding the semantic aspects that are relevant for our t...

We introduce the notion of an equational lifting monad: a commutative strong monad satisfying one additional equation (valid for monads arising from partial map classifiers). We prove that any equational lifting monad has a representation by a partial map classifier such that the Kleisli category of the former fully embeds in the partial category of the latter. Thus equational lifting monads pr...

For nite convergent term-rewriting systems the equational uniication problem is shown to be recursively independent of the equa-tional matching problem, the word matching problem, and the (simultaneous) 2 nd-order equational matching problem. We also present some new decidability results for simultaneous equational uniication and 2 nd-order equational matching.

In this paper we propose a complete axiomatization of the bisimilarity distance of Desharnais et al. for the class of finite labelled Markov chains. Our axiomatization is given in the style of a quantitative extension of equational logic recently proposed by Mardare, Panangaden, and Plotkin (LICS’16) that uses equality relations t ≡ε s indexed by rationals, expressing that “t is approximately e...

We present an approach for verifying dynamic systems specified in rewriting logic, a formal specification language implemented in the Maude system. Our approach is tailored for invariants, i.e., properties that hold on all states reachable from a given class of initial states. The approach consists in encoding invariance properties into inductive properties written in membership equational logi...

Many formal systems, particularly in computer science, may be captured by equations modulated by side conditions asserting the “freshness of names”; these can be reasoned about with Nominal Equational Logic (NEL). Like most logics of this sort NEL employs this notion of freshness as a first class logical connective. However, this can become inconvenient when attempting to translate results from...

The use of coalgebras for the speciication of dynamical systems with a hidden state space is receiving more and more attention in the years, as a valid alternative to algebraic methods based on observational equivalences. However, to our knowledge, the coalgebraic framework is still lacking a complete equational deduction calculus which enjoys properties similar to those stated in Birkhoo's com...

We present an approach based on inductive theorem proving for verifying invariants of dynamic systems specified in rewriting logic, a formal specification language implemented in the Maude system. An invariant is a property that holds on all the states that are reachable from a given class of initial states. Our approach consists in encoding the semantic aspects that are relevant for our task (...