We generalize the Constructor-based ReWriting Logic CRWL to the setting of the simply typed λ-calculus, where theories are presented by conditional overlapping fully extended pattern rewrite systems. We claim that this logic is useful for higher-order functional-logic programming, and propose a Higher-Order Lazy Narrowing calculus HOLNDT for answering joinability and reducibility queries, in wh...

We present a sequent calculus for intuitionistic non-commutative linear logic (INCLL), show that it satisfies cut elimination, and investigate its relationship to a natural deduction system for the logic. We show how normal natural deductions correspond to cut-free derivations, and arbitrary natural deductions to sequent derivations with cut. This gives us a syntactic proof of normalization for...

Suppose λ,x,ζ traverse the ordered sets Λ, X and Z, respectively and consider the functions f(λ,x,ζ) and g(λ,ζ) satisfying the following conditions, (a) f(λ,x,ζ) > 0 and f is TP2 in each pairs of variables when the third variable is held fixed and (b) g(λ,ζ) is TP2. Then the function h(λ,x) =∫Z f(λ,x,ζ)g(λ,ζ)dµ(ζ), defined on Λ×X is TP2 in (λ,x). The aim of this note is to use a new stochast...

For λ-terms constructed freely from a type signature in a type theory such as LF, there is a simple inductive subordination relation that is used to control type-formation. There is a related – but not precisely complementary – notion of independence that asserts that the inhabitants of the function space τ1 → τ2 depend vacuously on their arguments. Independence has many practical reasoning app...

We consider approximate policy evaluation for finite state and action Markov decision processes (MDP) with the least squares temporal difference (LSTD) algorithm, LSTD(λ), in an exploration-enhanced learning context, where policy costs are computed from observations of a Markov chain different from the one corresponding to the policy under evaluation. We establish for the discounted cost criter...

We describe Elf, a metalanguage for proof manipulation environments that are independent of any particular logical system. Elf is intended for meta-programs such as theorem provers, proof transformers, or type inference programs for programming languages with complex type systems. Elf unifies logic definition (in the style of LF, the Edinburgh Logical Framework) with logic programming (in the s...

This article proposes a general, intuitive and rigorous framework for designing temporal differences algorithms to solve optimal control problems in continuous time and space. Within this framework, we derive a version of the classical TD(λ) algorithm as well as a new TD algorithm which is similar, but designed to be more accurate and to converge as fast as TD(λ) for the best values of λ withou...

Bi-level programming techniques are developed to handle decentralized problems with two-level decision makers, leaders and followers, who may have more than one objective to achieve. This paper proposes a λ-cut and goal programming based algorithm to solve fuzzy linear multiple objective bi-level (FLMOB) decision problems. First, based on the definition of a distance measure between two fuzzy v...

We consider LSTD(λ), the least-squares temporal-difference algorithm with eligibility traces algorithm proposed by Boyan (2002). It computes a linear approximation of the value function of a fixed policy in a large Markov Decision Process. Under a β-mixing assumption, we derive, for any value of λ ∈ (0, 1), a high-probability bound on the rate of convergence of this algorithm to its limit. We d...

We study the Weak MSO logic in relationship to infinitary λ-calculus. We show that for every formula φ of Weak MSO there exists a finitary model of infinitary λ-calculus recognizing the set of infinitary λ-terms whose Böhm tree satisfies φ. The model is effective, in the sense that for every λY -term we can effectively compute its value in the model. In particular, given a finite λY -term, one ...