Journal of Applied Logic最新文献

There are two versions of type assignment in the λ-calculus: Church-style, in which the type of each variable is fixed, and Curry-style (also called “domain free”), in which it is not. As an example, in Church-style typing, ${\lambda }_{x:A}.x$ is the identity function on type A, and it has type $A\to A$ but not $B\to B$ for a type B different from A. In Curry-style typing, ${\lambda }_x.x$ is a general identity function with type $C\to C$ for every type C. In this paper, we will show how to interpret in a Curry-style system every Pure Type System (PTS) in the Church-style without losing any typing information. We will also prove a kind of conservative extension result for this interpretation, a result which implies that for most consistent PTSs of the Church-style, the corresponding Curry-style system is consistent. We will then show how to interpret in a system of the Church-style (a modified PTS, stronger than a PTS) every PTS-like system in the Curry style.

In this paper, we introduce hoop twist-structure whose members are built as special squares of an arbitrary hoop. We show how our construction relates to eN4-lattices (N4-lattices) and implicative twist-structures. We prove that hoop twist-structures form a quasi-variety and characterize the AHT-congruences of each algebra in this quasi-variety in terms of the congruences of the associated hoop.

Reliability has become an integral component of the design intent of embedded cyber-physical systems. Safety-critical embedded systems are designed with specific reliability targets, and design practices include the appropriate allocation of both spatial and temporal redundancies in the implementation to meet such requirements. With increasing complexity of such systems and considering the large number of components in such systems, redundancy allocation requires a formal scientific basis. In this work, we profess the analysis of the redundancy requirement upfront with the objective of making it an integral part of the specification. The underlying problem is one of synthesizing a formal specification with built-in redundancy artifacts, from the formal properties of the error-free system, the error probabilities of the control components, and the reliability target. We believe that upfront formal analysis of redundancy requirements is important in budgeting the resource requirements from a cost versus reliability perspective. Several case-studies from the automotive domain highlight the efficacy of our proposal.

A strongly polynomial sequence of graphs $\left(G_n\right)$ is a sequence ${\left(G_n\right)}_{n\in N}$ of finite graphs such that, for every graph F, the number of homomorphisms from F to $G_n$ is a fixed polynomial function of n (depending on F). For example, $\left(K_n\right)$ is strongly polynomial since the number of homomorphisms from F to $K_n$ is the chromatic polynomial of F evaluated at n. In earlier work of de la Harpe and Jaeger, and more recently of Averbouch, Garijo, Godlin, Goodall, Makowsky, Nešetřil, Tittmann, Zilber and others, various examples of strongly polynomial sequences and constructions for families of such sequences have been found, leading to analogues of the chromatic polynomial for fractional colourings and acyclic colourings, to choose two interesting examples.

We give a new model-theoretic method of constructing strongly polynomial sequences of graphs that uses interpretation schemes of graphs in more general relational structures. This surprisingly easy yet general method encompasses all previous constructions and produces many more. We conjecture that, under mild assumptions, all strongly polynomial sequences of graphs can be produced by the general method of quantifier-free interpretation of graphs in certain basic relational structures (essentially disjoint unions of transitive tournaments with added unary relations). We verify this conjecture for strongly polynomial sequences of graphs with uniformly bounded degree.

This article demonstrates that typical restrictions which are imposed in dialogical logic in order to recover first-order logical consequence from a fragment of natural language argumentation are also forthcoming from preference profiles of boundedly rational players, provided that these players instantiate a specific player type and compute partial strategies. We present two structural rules, which are formulated similarly to closure rules for tableaux proofs that restrict players' strategies to a mapping between games in extensive forms (i.e., game trees) and proof trees. Both rules are motivated from players' preferences and limitations; they can therefore be viewed as being player-self-imposable. First-order logical consequence is thus shown to result from playing a specific type of argumentation game. The alignment of such games with the normative model of the Pragma-dialectical theory of argumentation is positively evaluated. But explicit rules to guarantee that the argumentation game instantiates first-order logical consequence have now become gratuitous, since their normative content arises directly from players' preferences and limitations. A similar naturalization for non-classical logics is discussed.

Reliability Block Diagrams (RBDs) allow us to model the failure relationships of complex systems and their sub-components and are extensively used for system reliability, availability and maintainability analyses. Traditionally, these RBD-based analyses are done using paper-and-pencil proofs or computer simulations, which cannot ascertain absolute correctness due to their inaccuracy limitations. As a complementary approach, we propose to use the higher-order logic theorem prover HOL to conduct RBD-based analysis. For this purpose, we present a higher-order logic formalization of commonly used RBD configurations, such as series, parallel, parallel-series and series-parallel, and the formal verification of their equivalent mathematical expressions. A distinguishing feature of the proposed RBD formalization is the ability to model nested RBD configurations, which are RBDs having blocks that also represent RBD configurations. This generality allows us to formally analyze the reliability of many real-world systems. For illustration purposes, we formally analyze the reliability of a generic Virtual Data Center (VDC) in a cloud computing infrastructure exhibiting the nested series-parallel RBD configuration.

The heat pump with geothermal exchanger is one of the best methods to heat up a building. The heat exchanger is an element with high probability of failure due to the fact that it is an outside construction and also due to its size. In the present study, a novel intelligent system was designed to detect faults on this type of heating equipment. The novel approach has been successfully empirically tested under a real dataset obtained during measurements of one year. It was based on classification techniques with the aim of detecting failures in real time. Then, the model was validated and verified over the building; it obtained good results in all the operating conditions ranges.

We present a new prefixed tableau system $\mathrm{TK}$ for verification of validity in modal logic $K$. The system $\mathrm{TK}$ is deterministic, it uniquely generates exactly one proof tree for each clausal representation of formulas, and, moreover, it uses some syntactic reductions of prefixes. $\mathrm{TK}$ is defined in the original methodology of tableau systems, without any external technique such as backtracking, backjumping, etc. Since all the necessary bookkeeping is built into the rules, the system is not only a basis for a validity algorithm, but is itself a decision procedure. We present also a deterministic tableau decision procedure which is an extension of $\mathrm{TK}$ and can be used for the global assumptions problem.

The purpose of this document is to offer a combined approach in biometric analysis field, integrating some of the most known techniques using ears to recognize people. This study uses Hausdorff distance as a pre-processing stage adding sturdiness to increase the performance filtering for the subjects to use it in the testing process. Also includes the Image Ray Transform (IRT) and the Haar based classifier for the detection step. Then, the system computes Speeded Up Robust Features (SURF) and Linear Discriminant Analysis (LDA) as an input of two neural networks to recognize a person by the patterns of its ear. To show the applied theory experimental results, the above algorithms have been implemented using Microsoft C#. The investigation results showed robustness improving the ear recognition process.