Living Without Beth and Craig: Definitions and Interpolants in Description Logics with Nominals and Role Inclusions

The Craig interpolation property (CIP) states that an interpolant for an implication exists iff it is valid. The projective Beth definability property (PBDP) states that an explicit definition exists iff a formula stating implicit definability is valid. Thus, the CIP and PBDP transform potentially hard existence problems into deduction problems in the underlying logic. Description Logics with nominals and/or role inclusions do not enjoy the CIP nor PBDP, but interpolants and explicit definitions have many potential applications in ontology engineering and ontology-based data management. In this article we show the following: even without Craig and Beth, the existence of interpolants and explicit definitions is decidable in description logics with nominals and/or role inclusions such as ALCO, ALCH and ALCHIO. However, living without Craig and Beth makes this problem harder than deduction: we prove that the existence problems become 2ExpTime-complete, thus one exponential harder than validity. The existence of explicit definitions is 2ExpTime-hard even if one asks for a definition of a nominal using any symbol distinct from that nominal, but it becomes ExpTime-complete if one asks for a definition of a concept name using any symbol distinct from that concept name.Comment: We have added results on description logics with role inclusions and an ExpTime-completeness result for the explicit definability of concept names. The title has been modified by adding role inclusions. This paper has been accepted for AAAA 202

Living Without Beth and Craig: Definitions and Interpolants in Description and Modal Logics with Nominals and Role Inclusions

The Craig interpolation property (CIP) states that an interpolant for an implication exists iff it is valid. The projective Beth definability property (PBDP) states that an explicit definition exists iff a formula stating implicit definability is valid. Thus, the CIP and PBDP reduce potentially hard existence problems to entailment in the underlying logic. Description (and modal) logics with nominals and/or role inclusions do not enjoy the CIP nor the PBDP, but interpolants and explicit definitions have many applications, in particular in concept learning, ontology engineering, and ontology-based data management. In this article we show that, even without Beth and Craig, the existence of interpolants and explicit definitions is decidable in description logics with nominals and/or role inclusions such as $\mathcal {ALCO}$ , $\mathcal {ALCH}$ and $\mathcal {ALCHOI}$ and corresponding hybrid modal logics. However, living without Beth and Craig makes these problems harder than entailment: the existence problems become 2ExpTime-complete in the presence of an ontology or the universal modality, and coNExpTime-complete otherwise. We also analyze explicit definition existence if all symbols (except the one that is defined) are admitted in the definition. In this case the complexity depends on whether one considers individual or concept names. Finally, we consider the problem of computing interpolants and explicit definitions if they exist and turn the complexity upper bound proof into an algorithm computing them, at least for description logics with role inclusions. </jats:p

Advanced Strategies for Robot Manipulators

Amongst the robotic systems, robot manipulators have proven themselves to be of increasing importance and are widely adopted to substitute for human in repetitive and/or hazardous tasks. Modern manipulators are designed complicatedly and need to do more precise, crucial and critical tasks. So, the simple traditional control methods cannot be efficient, and advanced control strategies with considering special constraints are needed to establish. In spite of the fact that groundbreaking researches have been carried out in this realm until now, there are still many novel aspects which have to be explored

Contributions of synaptic filters to models of synaptically stored memory

The question of how neural systems encode memories in one-shot without immediately disrupting previously stored information has puzzled theoretical neuroscientists for years and it is the central topic of this thesis. Previous attempts on this topic, have proposed that synapses probabilistically update in response to plasticity inducing stimuli to effectively delay the degradation of old memories in the face of ongoing memory storage. Indeed, experiments have shown that synapses do not immediately respond to plasticity inducing stimuli, since these must be presented many times before synaptic plasticity is expressed. Such a delay could be due to the stochastic nature of synaptic plasticity or perhaps because induction signals are integrated before overt strength changes occur.The later approach has been previously applied to control fluctuations in neural development by low-pass filtering induction signals before plasticity is expressed. In this thesis we consider memory dynamics in a mathematical model with synapses that integrate plasticity induction signals to a threshold before expressing plasticity. We report novel recall dynamics and considerable improvements in memory lifetimes against a prominent model of synaptically stored memory. With integrating synapses the memory trace initially rises before reaching a maximum and then falls. The memory signal dissociates into separate oblivescence and reminiscence components, with reminiscence initially dominating recall. Furthermore, we find that integrating synapses possess natural timescales that can be used to consider the transition to late-phase plasticity under spaced repetition patterns known to lead to optimal storage conditions. We find that threshold crossing statistics differentiate between massed and spaced memory repetition patterns. However, isolated integrative synapses obtain an insufficient statistical sample to detect the stimulation pattern within a few memory repetitions. We extend the modelto consider the cooperation of well-known intracellular signalling pathways in detecting storage conditions by utilizing the profile of postsynaptic depolarization. We find that neuron wide signalling and local synaptic signals can be combined to detect optimal storage conditions that lead to stable forms of plasticity in a synapse specific manner.These models can be further extended to consider heterosynaptic and neuromodulatory interactions for late-phase plasticity.<br/

Abstract Homotopy Theory and the Thomason Model structure

There is a closed model structure on the category of small categories, called Thomason model structure, that is Quillen equivalent to the standard model structure on the category of topological spaces. We will give an introduction to the concepts necessary to understand the definition, as well as the purpose of the Thomason model structure. These concepts include category theory, classical homotopy theory on topological spaces, simplicial homotopy theory on simplicial sets and abstract homotopy theory via the use of model categories. We will show, that there is a model structure on the category of small acyclic categories, that is Quillen equivalent to the Thomason model structure. Both of these model structures share the same cofibrant objects, and we will show that these include finite semilattices, countable trees, finite zigzags and posets with five or less elements

A cultural study in the poetics of ecological consciousness: prolegomena to the poetry of John Burnside

This thesis -- originally entitled “Reckoning the Unnamed Fabric”, both a cultural study of the poetics of ecological consciousness and the ecology of poetic consciousness -- investigates the post-Romantic legacy informing John Burnside’s (b. 1955) poetry from The hoop (1988) to The Light Trap (2002) as a case study. The thesis argues that a developing aesthetic form and movement in subject derive from Burnside’s increasing involvement with ecological thought and practice. This move to the poetry of the oikos begins with an investigation of the self through the reconciliation of subject with object (or human with nature), and latterly has moved into a sustained reflection upon the idea of dwelling. This thesis relates the chronological development across Burnside’s nature poetry to an aesthetic infused with religious iconography and language, which via an evolving motif-poem of ‘world-soul’ or ‘communal fabric’ increases in its secular and empirical inflection. I read Burnside’s elevation of historical materialism s a progression in Wordsworthian craft and as a result of the poet’s pragmatic reflection on dwelling; I argue that the poetic consolidation of the intrinsic value of nature as an active and guiding spirit promotes nature less as a place for inhabitants than as the site and point of relation. The argument responds to Burnside’s transatlantic perspective from which he questions what it means to live as a spirit, and what a poetics of ecology can achieve in respect to the human subjective lyric and the need to transcend the human into the collective. To address these questions, which are implicit in Burnside's oeuvre, I draw upon Heideggerian poetics and American post-Transcendentalist Romanticism. I locate Burnside’s poetics within philosophical, aesthetic, and ecological frameworks. First, Burnside’s poetry is primarily a poetics of ontology that understands the ‘I’ within the midst of things yet underpinned by epistemology/hermeneutics; second, Burnside exhibits neo-Romantic poetry that has engaged with Modern American poetry -- it is this fusion that I call post-Romantic; third, the ecological constitutes both Burnside’s political stance and his aesthetic-poetic stance. I read the latter as a reflection of Jonathan Bate’s notion of the ecopoem as the “post-phenomenological inflection of high Romantic poetics”, an idea which is most apposite when read in relationship with Burnside’s path towards the metaphysical inscribed in the historical

Business Architecture Tool (BAT) : development and assessment of a systems framework to guide organisations from concept to delivery, in terms of creating deeper and meaningful integration across processes and functions

This thesis is based upon a prolonged research period, wherein a practical systems based tool (prototype), was researched, developed and tested, so as to gain outputs of integration improvements for service delivery in South Africa (SA) specifically, and in general for developmental economies. The research question can be summarised as: "to develop a systems-based intervention tool, able to provide practical integration improvements from concept to delivery". Existing systems methods and approaches were accessed, and based upon their utility for the local context, were used to varying degrees, in "building" the prototype, which was tested across a number of interventions, categorised under "world of the client"; and "world of the designer" (firm created for this purpose). Being aware of local and international implementation challenges by virtue of experience as consultant for a number of governments, whereby national planning and implementation techniques tend to be embed mechanistic models of thinking directly affecting how agents and agencies: understand the problem; plan to resolve the problem; and implement the designed solutions. The research sought to recover key systems insights in order to build a practical tool that could reduce negative outcomes, perpetrated by well-intended reforms, having limited integrative thinking, planning and delivery. The research required long-term observation, reflection, and extensive literature review. A distinctive feature of the research is the account of the author's exploration of his learning and development, within University of Cape Town PhD: Business Architecture embedded in complexity and systems theory