Branching Time Logics \mathcal {BTL}^{\mathrm {U,S}}_{\mathrm {N},\mathrm {N}^{-1}}(\mathcal {Z})_{\alpha } with Operations Until and Since Based on Bundles of Integer Numbers, Logical Consecutions, Deciding Algorithms

This paper is intended as an attempt to describe logical consequence in branching time logics. We study temporal branching time logics $\mathcal {BTL}^{\mathrm {U,S}}_{\mathrm {N},\mathrm {N}^{-1}}(\mathcal {Z})_{\alpha }$ which use the standard operations Until and Next and dual operations Since and Previous (LTL, as standard, uses only Until and Next). Temporal logics $\mathcal {BTL}^{\mathrm {U,S}}_{\mathrm {N},\mathrm {N}^{-1}}(\mathcal {Z})_{\alpha }$ are generated by semantics based on Kripke/Hinttikka structures with linear frames of integer numbers $\mathcal {Z}$ with a single node (glued zeros). For $\mathcal {BTL}^{\mathrm {U,S}}_{\mathrm {N},\mathrm {N}^{-1}}(\mathcal {Z})_{\alpha }$ , the permissible branching of the node is limited by α (where 1≤α≤ω). We prove that any logic $\mathcal {BTL}^{\mathrm {U,S}}_{\mathrm {N},\mathrm {N}^{-1}}(\mathcal {Z})_{\alpha }$ is decidable w.r.t. admissible consecutions (inference rules), i.e. we find an algorithm recognizing consecutions admissible in $\mathcal {BTL}^{\mathrm {U,S}}_{\mathrm {N},\mathrm {N}^{-1}}(\mathcal {Z})_{\alpha }$ . As a consequence, it implies that $\mathcal {BTL}^{\mathrm {U,S}}_{\mathrm {N},\mathrm {N}^{-1}}(\mathcal {Z})_{\alpha }$ itself is decidable and solves the satisfiability problem.     

Automata theory based on lattice-ordered semirings

In this paper, definitions of K{\mathcal{K}} automata, K{\mathcal{K}} regular languages, K{\mathcal{K}} regular expressions and K{\mathcal{K}} regular grammars based on lattice-ordered semirings are given. It is shown that K{\mathcal{K}}NFA is equivalent to K{\mathcal{K}}DFA under some finite condition, the Pump Lemma holds if K{\mathcal{K}} is finite, and Ke{{\mathcal{K}}}\epsilonNFA is equivalent to K{\mathcal{K}}NFA. Further, it is verified that the concatenation of K{\mathcal{K}} regular languages remains a K{\mathcal{K}} regular language. Similar to classical cases and automata theory based on lattice-ordered monoids, it is also found that K{\mathcal{K}}NFA, K{\mathcal{K}} regular expressions and K{\mathcal{K}} regular grammars are equivalent to each other when K{\mathcal{K}} is a complete lattice.     

Meta-logic programming for a synonymy logic

In order to give a suitable framework for a synonymy-based logic programming, we argue about the possibility of reducing fuzzy logic programming to classical logical programming. More precisely, we show that given a fuzzy program in a language L, we can translate it into an equivalent classical program in a (meta-)language \textL_m {\text{L}}_{m} in which every predicate name in L becomes a constant in \textL_m . {\text{L}}_{m} . This enables us to admit in \textL_m {\text{L}}_{m} meta-relations among predicates and therefore, in particular, the synonymy.     

The <Emphasis Type="Italic">k</Emphasis>-Homotopic Thinning and a Torus-Like Digital Image in <Emphasis Type="Bold">Z</Emphasis><Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>

In order to discuss digital topological properties of a digital image (X,k), many recent papers have used the digital fundamental group and several digital topological invariants such as the k-linking number, the k-topological number, and so forth. Owing to some difficulties of an establishment of the multiplicative property of the digital fundamental group, a k-homotopic thinning method can be essentially used in calculating the digital fundamental group of a digital product with k-adjacency. More precisely, let be a simple closed k _i -curve with l _i elements in . For some k-adjacency of the digital product which is a torus-like set, proceeding with the k-homotopic thinning of , we obtain its k-homotopic thinning set denoted by DT _k . Writing an algorithm for calculating the digital fundamental group of , we investigate the k-fundamental group of by the use of various properties of a digital covering (Z×Z,p ₁×p ₂,DT _k ), a strong k-deformation retract, and algebraic topological tools. Finally, we find the pseudo-multiplicative property (contrary to the multiplicative property) of the digital fundamental group. This property can be used in classifying digital images from the view points of both digital k-homotopy theory and mathematical morphology.

Prediction of phosphorus content of electroless nickel–phosphorous coatings using artificial neural network modeling

A multilayer feedforward neural network with two hidden layers was designed and developed for prediction of the phosphorus content of electroless Ni–P coatings. The input parameters of the network were the pH, metal turnover, and loading of an electroless bath. The output parameter was the phosphorus content of the electroless Ni–P coatings. The temperature and molar rate of the bath were constant ( 91^° \textC, 0.4 \textNi^{\text + +} /\textH₂ \textPO₂ ^{- -} 91^\circ {\text{C}},\:0.4\,{\text{Ni}}^{{{\text{ + + }}}} /{\text{H}}_{2} {\text{PO}}_{2}^{{ - - }} ). The network was trained and tested using the data gathered from our own experiments. The goal of the study was to estimate the accuracy of this type of neural network in prediction of the phosphorus content. The study result shows that this type of network has high accuracy even when the number of hidden neurons is very low. Some comparison between the network’s predictions and own experimental data are given.     

Takagi–Sugeno Fuzzy Hopfield Neural Networks for $${\mathcal{H}_{\infty}}$$ Nonlinear System Identification

In this paper, we propose a new H_￥{\mathcal H_\infty} weight learning algorithm (HWLA) for nonlinear system identification via Takagi–Sugeno (T–S) fuzzy Hopfield neural networks with time-delay. Based on Lyapunov stability theory, for the first time, the HWLA for nonlinear system identification is presented to reduce the effect of disturbance to an H_￥{\mathcal{H}_{\infty }} norm constraint. The HWLA can be obtained by solving a convex optimization problem which is represented in terms of linear matrix inequality (LMI). An illustrative example is given to demonstrate the effectiveness of the proposed identification scheme.     

The 1-Versus-2 Queries Problem Revisited

The 1-versus-2 queries problem, which has been extensively studied in computational complexity theory, asks in its generality whether every efficient algorithm that makes at most 2 queries to a Σ _k ^p -complete language L _k has an efficient simulation that makes at most 1 query to L _k . We obtain solutions to this problem for hypotheses weaker than previously considered. We prove that:

Lower Bounds for Agnostic Learning via Approximate Rank

We prove that the concept class of disjunctions cannot be pointwise approximated by linear combinations of any small set of arbitrary real-valued functions. That is, suppose that there exist functions f₁, ?, f_r\phi_{1}, \ldots , \phi_{r} : {− 1, 1}ⁿ → \mathbbR{\mathbb{R}} with the property that every disjunction f on n variables has $\|f - \sum\nolimits_{i=1}^{r} \alpha_{i}\phi _{i}\|_{\infty}\leq 1/3$\|f - \sum\nolimits_{i=1}^{r} \alpha_{i}\phi _{i}\|_{\infty}\leq 1/3 for some reals a₁, ?, a_r\alpha_{1}, \ldots , \alpha_{r}. We prove that then $r \geq exp \{\Omega(\sqrt{n})\}$r \geq exp \{\Omega(\sqrt{n})\}, which is tight. We prove an incomparable lower bound for the concept class of decision lists. For the concept class of majority functions, we obtain a lower bound of W(2ⁿ/n)\Omega(2^{n}/n) , which almost meets the trivial upper bound of 2ⁿ for any concept class. These lower bounds substantially strengthen and generalize the polynomial approximation lower bounds of Paturi (1992) and show that the regression-based agnostic learning algorithm of Kalai et al. (2005) is optimal.     

Engineering and verifying agent-oriented requirements augmented by business constraints with $${\mathcal{B}}$$-Tropos

We propose B{\mathcal{B}}-Tropos as a modeling framework to support agent-oriented systems engineering, from high-level requirements elicitation down to execution-level tasks. In particular, we show how B{\mathcal{B}}-Tropos extends the Tropos methodology by means of declarative business constraints, inspired by the ConDec graphical language. We demonstrate the functioning of B{\mathcal{B}}-Tropos using a running example inspired by a real-world industrial scenario, and we describe how B{\mathcal{B}}-Tropos models can be automatically formalized in computational logic, discussing formal properties of the resulting framework and its verification capabilities.     

Non-determinism in Gödel’s System <Emphasis Type="Italic">T</Emphasis>

The calculus T^? is a successor-free version of Gödel’s T. It is well known that a number of important complexity classes, like e.g. the classes logspace, \(\textsc{p}\), \(\textsc{linspace}\), \(\textsc{etime}\) and \(\textsc{pspace}\), are captured by natural fragments of T^? and related calculi. We introduce the calculus T^∽, which is a non-deterministic variant of T^?, and compare the computational power of T^∽ and T^?. First, we provide a denotational semantics for T^∽ and prove this semantics to be adequate. Furthermore, we prove that \(\textsc{linspace}\subseteq \mathcal {G}^{\backsim }_{0} \subseteq \textsc{linspace}\) and \(\textsc{etime}\subseteq \mathcal {G}^{\backsim }_{1} \subseteq \textsc{pspace}\) where \(\mathcal {G}^{\backsim }_{0}\) and \(\mathcal {G}^{\backsim }_{1}\) are classes of problems decidable by certain fragments of T^∽. (It is proved elsewhere that the corresponding fragments of T^? equal respectively \(\textsc{linspace}\) and \(\textsc{etime}\).) Finally, we show a way to interpret T^∽ in T^?.     

Speeding up simplification of polygonal curves using nested approximations

We develop a top-down multiresolution algorithm (TDMR) to solve iteratively the problem of polygonal curve approximation. This algorithm provides nested polygonal approximations of an input curve. We show theoretically and experimentally that, if the simplification algorithm A{\mathcal{A}} used between any two successive levels of resolution satisfies some conditions, the multiresolution algorithm will have a complexity lower than the complexity of A{\mathcal{A}} applied directly on the input curve to provide the crudest polygonal approximation. In particular, we show that if A{\mathcal{A}} has a O(N ²/K) complexity (the complexity of a reduced search dynamic programming solution approach), where N and K are, respectively, the number of segments in the input curve and the number of segments in the crudest approximation, the complexity of MR is in O(N). We experimentally compare the outcomes of TDMR with those of the optimal full search dynamic programming solution and of classical merge and split approaches. The experimental evaluations confirm the theoretical derivations and show that the proposed approach evaluated on 2D coastal maps either leads to a lower complexity or provides polygonal approximations closer to the initial curves.     

A Dynamic Logic of Agency II: Deterministic $${\mathcal{DLA}}$$ , Coalition Logic,and Game Theory

We continue the work initiated in Herzig and Lorini (J Logic Lang Inform, in press) whose aim is to provide a minimalistic logical framework combining the expressiveness of dynamic logic in which actions are first-class citizens in the object language, with the expressiveness of logics of agency such as STIT and logics of group capabilities such as CL and ATL. We present a logic called DDLA{\mathcal{DDLA}} (Deterministic Dynamic logic of Agency) which supports reasoning about actions and joint actions of agents and coalitions, and agentive and coalitional capabilities. In DDLA{\mathcal{DDLA}} it is supposed that, once all agents have selected a joint action, the effect of this joint action is deterministic. In order to assess DDLA{\mathcal{DDLA}} we prove that it embeds Coalition Logic. We then extend DDLA{\mathcal{DDLA}} with modal operators for agents’ preferences, and show that the resulting logic is sufficiently expressive to capture the game-theoretic concepts of best response and Nash equilibrium.     

Strong non-standard completeness for fuzzy logics

In this paper we are going to introduce the notion of strong non-standard completeness (SNSC) for fuzzy logics. This notion naturally arises from the well known construction by ultraproduct. Roughly speaking, to say that a logic is strong non-standard complete means that, for any countable theory Γ over and any formula φ such that , there exists an evaluation e of -formulas into a -algebra such that the universe of is a non-Archimedean extension of the real unit interval [0,1], e is a model for Γ, but e(φ) < 1. Then we will apply SNSC to prove that various modal fuzzy logics allowing to deal with simple and conditional probability of infinite-valued events are complete with respect to classes of models defined starting from non-standard measures, that is measures taking value in .     

On Projection Matrices $$\mathcal{P}^k \to \mathcal{P}^2 ,k = 3,...,6, $$ and their Applications in Computer Vision

Projection matrices from projective spaces have long been used in multiple-view geometry to model the perspective projection created by the pin-hole camera. In this work we introduce higher-dimensional mappings for the representation of various applications in which the world we view is no longer rigid. We also describe the multi-view constraints from these new projection matrices (where k > 3) and methods for extracting the (non-rigid) structure and motion for each application.     

Weakly coprime factorization and state-feedback stabilization of discrete-time systems

The LQ-optimal state feedback of a finite-dimensional linear time-invariant system determines a coprime factorization NM ⁻¹ of the transfer function. We show that the same is true also for infinite-dimensional systems over arbitrary Hilbert spaces, in the sense that the factorization is weakly coprime, i.e., Nf, for every function f. The factorization need not be Bézout coprime. We prove that every proper quotient of two bounded holomorphic operator-valued functions can be presented as the quotient of two bounded holomorphic weakly coprime functions. This result was already known for matrix-valued functions with the classical definition gcd(N, M) = I, which we prove equivalent to our definition. We give necessary and sufficient conditions and further results for weak coprimeness and for Bézout coprimeness. We then establish a variant of the inner–outer factorization with the inner factor being “weakly left-invertible”. Most of our results hold also for continuous-time systems and many are new also in the scalar-valued case.