We build a logical system named a conjunctive sequent calculus which is a conjunctive fragment of the classical propositional sequent calculus in the sense of proof theory. We prove that a special class of formulae of a consistent conjunctive sequent calculus forms a bounded complete continuous domain without greatest element (for short, a proper BC domain), and each proper BC domain can be obtained in this way. More generally, we present conjunctive consequence relations as morphisms between consistent conjunctive sequent calculi and build a category which is equivalent to that of proper BC domains with Scott-continuous functions. A logical characterization of purely syntactic form for proper BC domains is obtained.

The progressive automation framework allows the seamless transition of a robot from kinesthetic guidance to autonomous operation mode during programming by demonstration of discrete motion tasks. This is achieved by the synergetic action of dynamic movement primitives (DMPs), virtual fixtures, and variable impedance control. The proposed DMPs encode the demonstrated trajectory and synchronize with the current demonstration from the user so that the reference generated motion follows the human’s demonstration. The proposed virtual fixtures assist the user in repeating the learned kinematic behavior but allow penetration so that the user can make modifications to the learned trajectory if needed. The tracking error in combination with the interaction forces and torques is used by a variable stiffness strategy to adjust the progressive automation level and transition the leading role between the human and the robot. An energy tank approach is utilized to apply the designed controller and to prove the passivity of the overall control method. An experimental evaluation of the proposed framework is presented for a pick and place task and results show that the transition to autonomous mode is achieved in few demonstrations.

For $$\tau \in {S_3}$$, let $$\mu _n^\tau $$ denote the uniformly random probability measure on the set of $$\tau $$-avoiding permutations in $${S_n}$$. Let $${\mathbb {N}^*} = {\mathbb {N}} \cup \{ \infty \} $$ with an appropriate metric and denote by $$S({\mathbb{N}},{\mathbb{N}^*})$$ the compact metric space consisting of functions $$\sigma {\rm{= }}\{ {\sigma _i}\} _{i = 1}^\infty {\rm{}}$$ from $$\mathbb {N}$$ to $${\mathbb {N}^ * }$$ which are injections when restricted to $${\sigma ^{ - 1}}(\mathbb {N})$$; that is, if $${\sigma _i}{\rm{= }}{\sigma _j}$$, $$i \ne j$$, then $${\sigma _i} = \infty $$. Extending permutations $$\sigma \in {S_n}$$ by defining $${\sigma _j} = j$$, for $$j \gt n$$, we have $${S_n} \subset S({\mathbb{N}},{{\mathbb{N}}^*})$$. For each $$\tau \in {S_3}$$, we study the limiting behaviour of the measures $$\{ \mu _n^\tau \} _{n = 1}^\infty $$ on $$S({\mathbb{N}},{\mathbb{N}^*})$$. We obtain partial results for the permutation $$\tau= 321$$ and complete results for the other five permutations $$\tau \in {S_3}$$.

One problem in incremental product development is that geometric models are limited in their ability to explore radical alternative design variants. In this publication, a function modeling approach is suggested to increase the amount and variety of explored alternatives, since function models (FM) provide greater model flexibility. An enhanced function-means (EF-M) model capable of representing the constraints of the design space as well as alternative designs is created through a reverse engineering process. This model is then used as a basis for the development of a new product variant. This work describes the EF-M model's capabilities for representing the design space and integrating novel solutions into the existing product structure and explains how these capabilities support the exploration of alternative design variants. First-order analyses are executed, and the EF-M model is used to capture and represent already existing design information for further analyses. Based on these findings, a design space exploration approach is developed. It positions the FM as a connection between legacy and novel designs and, through this, allows for the exploration of more diverse product concepts. This approach is based on three steps – decomposition, design, and embodiment – and builds on the capabilities of EF-M to model alternative solutions for different requirements. While the embodiment step of creating the novel product's geometry is still a topic for future research, the design space exploration concept can be used to enable wider, more methodological, and potentially automated design space exploration.

This paper formally compares some central notions from two well-known formalisms for rule-based argumentation, DeLP and ASPIC+. The comparisons especially focus on intuitive adequacy and inter-translatability, consistency, and closure properties. As for differences in the definitions of arguments and attack, it turns out that DeLP’s definitions are intuitively appealing but that they may not fully comply with Caminada and Amgoud’s rationality postulates of strict closure and indirect consistency. For some special cases, the DeLP definitions are shown to fare better than ASPIC+. Next, it is argued that there are reasons to consider a variant of DeLP with grounded semantics, since in some examples its current notion of warrant arguably has counterintuitive consequences and may lead to sets of warranted arguments that are not admissible. Finally, under some minimality and consistency assumptions on ASPIC+ arguments, a one-to-many correspondence between ASPIC+ arguments and DeLP arguments is identified in such a way that if the DeLP warranting procedure is changed to grounded semantics, then ’s DeLP notion of warrant and ASPIC+ ’s notion of justification are equivalent. This result is proven for three alternative definitions of attack.

We present a method for mining the web for text entered on mobile devices. Using searching, crawling, and parsing techniques, we locate text that can be reliably identified as originating from 300 mobile devices. This includes 341,000 sentences written on iPhones alone. Our data enables a richer understanding of how users type “in the wild” on their mobile devices. We compare text and error characteristics of different device types, such as touchscreen phones, phones with physical keyboards, and tablet computers. Using our mined data, we train language models and evaluate these models on mobile test data. A mixture model trained on our mined data, Twitter, blog, and forum data predicts mobile text better than baseline models. Using phone and smartwatch typing data from 135 users, we demonstrate our models improve the recognition accuracy and word predictions of a state-of-the-art touchscreen virtual keyboard decoder. Finally, we make our language models and mined dataset available to other researchers.

We prove that, for q odd, a set of q + 2 points in the projective plane over the field with q elements has at least 2q − c odd secants, where c is a constant and an odd secant is a line incident with an odd number of points of the set.

Rewriting logic is naturally concurrent: several subterms of the state term can be rewritten simultaneously. But state terms are global, which makes compositionality difficult to achieve. Compositionality here means being able to decompose a complex system into its functional components and code each as an isolated and encapsulated system. Our goal is to help bringing compositionality to system specification in rewriting logic. The base of our proposal is the operation that we call synchronous composition. We discuss the motivations and implications of our proposal, formalize it for rewriting logic and also for transition structures, to be used as semantics, and show the power of our approach with some examples.

In recent work, Stalnaker proposes a logical framework in which belief is realized as a weakened form of knowledge 35. Building on Stalnaker’s core insights, and using frameworks developed in 11 and 3, we employ topological tools to refine and, we argue, improve on this analysis. The structure of topological subset spaces allows for a natural distinction between what is known and (roughly speaking) what is knowable; we argue that the foundational axioms of Stalnaker’s system rely intuitively on both of these notions. More precisely, we argue that the plausibility of the principles Stalnaker proposes relating knowledge and belief relies on a subtle equivocation between an “evidence-in-hand” conception of knowledge and a weaker “evidence-out-there” notion of what could come to be known. Our analysis leads to a trimodal logic of knowledge, knowability, and belief interpreted in topological subset spaces in which belief is definable in terms of knowledge and knowability. We provide a sound and complete axiomatization for this logic as well as its uni-modal belief fragment. We then consider weaker logics that preserve suitable translations of Stalnaker’s postulates, yet do not allow for any reduction of belief. We propose novel topological semantics for these irreducible notions of belief, generalizing our previous semantics, and provide sound and complete axiomatizations for the corresponding logics.

This note shows that the permutation instructions presented by Zardini (2011) for eliminating cuts on universally quantified formulas in the sequent calculus for the noncontractive theory of truth IKTω are inadequate. To that purpose the note presents a derivation in the sequent calculus for IKTω ending with an application of cut on a universally quantified formula which the permutation instructions cannot deal with. The counterexample is of the kind that leaves open the question whether cut can be shown to be eliminable in the sequent calculus for IKTω with an alternative strategy.

Motivated by the work of Razborov about the minimal density of triangles in graphs we study the minimal density of the 5-cycle C5. We show that every graph of order n and size $ (1 - 1/k) \left( {\matrix{n \cr 2 }} \right) $, where k ≥ 3 is an integer, contains at least

$$({1 \over {10}} - {1 \over {2k}} + {1 \over {{k^2}}} - {1 \over {{k^3}}} + {2 \over {5{k^4}}}){n^5} + o({n^5})$$

In the traditional Axiomatic Design (AD) theory, the mapping from the functional domain to the physical domain is based on the designers’ own knowledge and experience, and there is no systematical approach including the design resources provided outside the designers themselves’ access. Thus, the raw materials for the design process are largely limited, which means they can hardly support the designers’ increasingly creative and innovative conceptions. To help AD theory better support the design process, this paper proposes a computer-aided approach for the mapping from the functional domain to the physical domain within a distributed design resource environment, which consists of numerous design resources offered on the Internet by the providers widely distributed in different locations, institutes, and disciplines. To prove the feasibility of this proposed approach, a software prototype is established, and a natural leisure hotel is designed as an implementation case.