We study interior Lp-regularity theory, also known as Calderon-Zygmund of the equation〈Lsu,φ〉:=∫Rn∫RnK(x,y)(u(x)−u(y))(φ(x)−φ(y))|x−y|n+2sdxdy=〈f,φ〉,∀φ∈Cc∞(Rn). prove that for s∈(0,1), t∈[s,2s], p∈[2,∞), K an elliptic, symmetric, and K(⋅,y) is uniformly Hölder continuous, solution u belongs to Hloc2s−t,p(Ω) long 2s−t<1 f∈(H00t,p′(Ω))⁎. The increase in differentiability integrability independent...

Planning as satisfiability, as implemented in, for instance, the SATPLAN tool, is a highly competitive method for finding parallel step-optimal plans. A bottleneck in this approach is to prove the absence of plans of a certain length. Specifically, if the optimal plan has n steps, then it is typically very costly to prove that there is no plan of length n−1. We pursue the idea of leading this p...

Model checking ([7, 13], c.f.[6]) is a technique for verifying finite-state concurrent systems that has proven effective in the verification of industrial hardware and software programs. In model checking, a model M , given as a set of state variables V and their next-state relations, is verified against a temporal logic formula φ. In this work we consider only safety formulas of the form AG(b)...

In this paper we introduce a new formal model, called finite state machines with time (FSMT), to represent real-time systems. We present a model checking algorithm for FSMTs, which works on fully symbolic state sets containing both the clock values and the state variables. Besides complete networks of FSMTs our algorithm can verify incomplete real-time systems in form of incomplete FSMTs, and i...

We investigate modal logical aspects of provability predicates PrT(x) satisfying the following condition: M: If T⊢φ→ψ, then T⊢PrT(⌜φ⌝)→PrT(⌜ψ⌝). prove arithmetical completeness theorems for monotonic logics MN, MN4, MNP, MNP4, and MND with respect to condition M. That is, we that each logic L them, there exists a Σ1 predicate M such is exactly L. In particular, formulas P: ¬□⊥ D: ¬(□A∧□¬A) are ...

Well-posedness of constrained minimization problems via saddle-points BIAGIO RICCERI Dedicated to Professor Jean Saint Raymond on his sixtieth birthday, with my greatest admiration and esteem Here and in the sequel, X is a Hausdorff topological space, J, Φ are two real-valued functions defined in X, and a, b are two numbers in [−∞, +∞], with a < b.

The unification problem in a propositional logic is to determine, given formula φ, whether there exists substitution σ such that σ(φ) logic. In case, unifier of φ. When unifiable has minimal complete sets unifiers, it either infinitary, finitary, or unitary, depending on the cardinality its unifiers. Otherwise, nullary. this paper, we prove modal $\mathbf {K}+\square \square \bot $ , formulas a...