信任本体的形式化语义研究

针对现有的信任模型缺少信任相关概念属性在数理上的定义以及严格可靠的信任语义推理和统一的形式化抽象模型的问题,本文提出形式化动态信任本体的概念,结合本体在语义层次的形式化描述方法,对实体信任、行为信任和区域信任进行本体化,并对三种信任本体进行形式化语义演绎和推理.给出了信任相关属性的形式化理论分析,并通过典型的激发场景实例,有效地验证了信任本体化理论.     

Dual‐Context Sequent Calculus and Strict Implication

We introduce a dual‐context style sequent calculus which is complete with respectto Kripke semantics where implication is interpreted as strict implication in the modal logic K. The cut‐elimination theorem for this calculus is proved by a variant of Gentzen's method.     

网络驱动的未识甲骨字特性及场景语义预测

甲骨学的研究具有重要的文化价值和传承意义,可以极大提高国家的文化自信。未识甲骨字的语义预测是甲骨学研究中最主要的问题,也是传统甲骨学研究中最棘手的问题。现有的计算机技术辅助研究方法无法预测未识甲骨字的语义。利用复杂网络对甲骨文进行了抽象和理解,并对未识甲骨字的场景语义进行预测。首先,以甲骨拓片为基础数据,通过建模构建甲骨字网络;其次,在甲骨字网络之上,分析未识甲骨字的重要性、信息丰富度、闭合性等特性,为预测未识甲骨字的场景语义提供理论依据;最后,根据网络特性和甲骨拓片的上下文语境预测未识甲骨字的场景语义。构建的未识甲骨字特性体系以及预测未识甲骨字的场景语义思路为破译其他未识甲骨字的语义奠定了基础,有助于推动甲骨文考释的进程。     

The expressive power of k-ary exclusion logic

In this paper we study the expressive power of k-ary exclusion logic, EXC[k], that is obtained by extending first order logic with k-ary exclusion atoms. It is known that without arity bounds exclusion logic is equivalent with dependence logic. By observing the translations, we see that the expressive power of EXC[k] lies in between k-ary and ($k+1$)-ary dependence logics. We will show that, at least in the case when $k=1$, both of these inclusions are proper.In a recent work by the author it was shown that k-ary inclusion-exclusion logic is equivalent with k-ary existential second order logic, ESO[k]. We will show that, on the level of sentences, it is possible to simulate inclusion atoms with exclusion atoms, and in this way express ESO[k]-sentences by using only k-ary exclusion atoms. For this translation we also need to introduce a novel method for “unifying” the values of certain variables in a team. As a consequence, EXC[k] captures ESO[k] on the level of sentences, and we obtain a strict arity hierarchy for exclusion logic. It also follows that k-ary inclusion logic is strictly weaker than EXC[k].Finally we use similar techniques to formulate a translation from ESO[k] to k-ary inclusion logic with an alternative strict semantics. Consequently, for any arity fragment of inclusion logic, strict semantics is strictly more expressive than lax semantics.     

Quantum Uncertainties and Holism Seem to Render Irrelevant Qudit-Semantics

We consider a semantics based on the peculiar holistic features of the quantum formalism. Any formula of the language gives rise to a quantum circuit that transforms the density operator associated to the formula into the density operator associated to the atomic subformulas in a reversible way. The procedure goes from the whole to the parts against the compositionality-principle and gives rise to a semantic characterization for a new form of quantum logic that has been called “Łukasiewicz quantum computational logic”. It is interesting to compare the logic based on qubit-semantics with that on qudit-semantics. Having in mind the relationships between classical logic and Łukasiewicz-many valued logics, one could expect that the former is stronger than the fragment of the latter. However, this is not the case. From an intuitive point of view, this can be explained by recalling that the former is a very weak form of logic. Many important logical arguments, which are valid either in Birkhoff and von Neumann’s quantum logic or in classical logic, are generally violated.     

线性逻辑和态极逻辑引论(Ⅰ)

《线性逻辑和态极逻辑引论》一文概述了由Girard分别于1986和2001所创建的线性逻辑和态极逻辑.线性逻辑和态极逻辑汲取于计算机科学并反之应用于其中,从根本上对数理逻辑进行了彻底的审视.全文分为两部分.本文是文章的第一部分,致力于线性逻辑的联结词、证明规则、可判定性性质和模型.文章的第二部分将研究证明网并简要介绍态极逻辑.证明网是证明的图式表示,是线性逻辑的主要创新之一.     

Looking-ahead in backtracking algorithms for abstract argumentation

We refine implemented backtracking algorithms for a number of problems related to Dung's argumentation frameworks. Under admissible, preferred, complete, stable, semi stable, and ideal semantics we add enhancements, what are so-called global looking-ahead pruning strategies, to the-state-of-the-art implementations of two problems. First, we tackle the extension enumeration problem: constructing some/all set(s) of acceptable arguments of a given argumentation framework. Second, we address the acceptance decision problem: deciding whether an argument is in some/all set(s) of accepted arguments of a given argumentation framework. The experiments that we report show that the speedup gain of the new enhancements is quite significant.     

Filtrations of generalized Veltman models

The filtration method is often used to prove the finite model property of modal logics. We adapt this technique to the generalized Veltman semantics for interpretability logics. In order to preserve the defining properties of generalized Veltman models, we use bisimulations to define adequate filtrations. We give an alternative proof of the finite model property of interpretability logic with respect to Veltman models, and we prove the finite model property of the systems and with respect to generalized Veltman models.     

Topological cones: functional analysis in a T<Subscript>0</Subscript>-setting

Already in his PhD Thesis on compact Abelian semigroups under the direction of Karl Heinrich Hofmann the author was lead to investigate locally compact cones (Keimel in Math. Z. 99:205–428, 1967). This happened in the setting of Hausdorff topologies. The theme of topological cones has been reappearing in the author’s work in a non-Hausdorff setting motivated by the needs of mathematical models for a denotational semantics of languages combining probabilistic and nondeterministic choice. This is in the line of common work with Karl Heinrich Hofmann in Continuous Lattices and Domains (Gierz et al. in Encyclopedia of Mathematics and its Applications, vol. 93, 2003). Domain Theory is based on order theoretical notions from which intrinsic non-Hausdorff topologies are derived. Along these lines, domain theoretical variants of (sub-) probability measures have been introduced by Jones and Plotkin (Jones, PhD thesis, 1990; Jones and Plotkin in Proceedings of the Fourth Annual Symposium on Logic in Computer Science, pp. 186–195, 1989). Kirch (Master’s thesis, 1993) and Tix (Master’s thesis, 1995) have extended this theory to a domain theoretical version of measures and they have introduced and studied directed complete partially ordered cones as appropriate structures. Driven by the needs of a semantics for languages combining probability and nondeterminism, Tix (Theor. Comput. Sci 264:205–218, 1999; PhD thesis, 1999) and later on Plotkin and Keimel (Electron. Notes Theor. Comput. Sci. 129:1–104, 2005) developed basic functional analytic tools for these structures. In this paper we extend this theory to topological cones the topologies of which are strongly non-Hausdorff. We carefully introduce these structures and their elementary properties. We prove Hahn-Banach type separation theorems under appropriate local convexity hypotheses. We finally construct a monad assigning to every topological cone C another topological cone the elements of which are nonempty compact convex subsets of C. For proving that this construction has good properties needed for the application in semantics we use the functional analytic tools developed before. Dedicated to Karl Heinrich Hofmann at the occasion of his 75th birthday. Thanks to Gordon Plotkin for numerous discussions. Preliminary results have been announced at MFPS XXIII 20. In his Master’s thesis supervised by the author, B. Cohen 6 has worked out some of those results.