Connections between default-assumption and preferential approaches to defeasible reasoning

Owing to the research program of Artificial Intelligence, in the last decades a big effort has been undertaken in order to develop interesting models of human reasoning by means of logical tools, receiving contributions from various fields, as Philosophy, Mathematics and Computer Science. One of the main problems has been the characterization of defeasible inference, i.e. that kind of inference, modeling common-sense reasoning, in which an agent draws tentative conclusions, using as supplementary information what he maintains as holding in most normal situations. Such conclusions are open to revision in case more complete information about the actual situation becomes available to the agent. This thesis focusses on defeasible logics (or nonmonotonic logics). In particular we analyze the connection between two of the main approaches to the formalization of defeasible reasoning: the default-assumption and the preferential formalizations. On the basis of such connection we can have a deeper understanding of both approaches, and use the tools provided by each approach to work in the other one. In the first two chapters the thesis presents the main problems and the main formal approaches to the development of logical models for defeasible reasoning. We briefly present the main proposals in the field of nonmonotonic logics and delineate the consequentialist view to the study of defeasible reasoning, i.e. an approach focused on the analysis of the behaviour of the inference relations generated by the different types of logical systems. In particular, following the recent literature, we delineate three main views, the default-assumption, preferential and default-rule approaches, distinguished by the kind of formalization used to represent default information (i.e. information about what normally holds). In the third chapter we show that there is a correspondence between the basic formulations of the three different approaches, in particular stressing a strong connection between the preferential and the default-assumption ones, the former referring to a preference order defined over the set of the semantic valuations of the language, the latter using a set of formulae as background information, to be added to actual information as extra-premises. We shall refer to such a connection all along the thesis. The fourth chapter is dedicated to a brief presentation of the main results in the study of defeasible reasoning from a consequentialist point of view, presenting the main representation theorems, relating the satisfaction of desirable properties of the inference relations to particular classes of preferential models. In the fifth chapter we isolate an interesting class of inference relations, weakly rational inference relations, that we shall use in the following chapters, and prove a representation theorem connecting such inference relations to the class of optimal preferential models. The content of the sixth chapter is directly connected to the correspondence between the default-assumption and the preferential approach: we show how it is possible to use the default-assumption approach in order to build interesting preferential models, defining well-behaved inference relations. In the seventh chapter we use the correspondence between default-assumption and preferential approaches in order to define in a precise way the behaviour of default formulae, by means of a normality operator. In the end of the chapter we present a generalization of a model of stereotypical reasoning proposed by Lehmann. In the last chapter we move into the field of belief revision, defining a possible approach to the revision of default information, referring as a starting point to the main results of the AGM approach, one of the cornerstones in the field

Localization and function of GABA transporter 1 in the retina

Plasma membrane transporters, located in the presynaptic terminal and/or surrounding glial cells, terminate synaptic transmission by operating rapid, high affinity uptake of the neurotransmitter from the synaptic cleft. Pharmacological blockade of transporters increases extracellular neurotransmitter levels and prolongs transmitter exposure to the receptors. GABA transporters (GATs) belong to the Na+ and Cl--dependent transporter family. Four GATs have been isolated and cloned in mammals. Of them, GAT-1 and GAT-3 are expressed in the retina. GAT-1 has a widespread distribution to different retinal cell types, but it is prominently expressed in amacrine cells of all vertebrate species studied to date. There are some species differences in the expression patterns of GAT-1 in the retina. It is expressed by horizontal cells in non-mammalian but not in mammalian retinas, and it is expressed in Müller glial cells of rats and guinea pigs, but not of rabbits and primates. Functionally, GAT-1, together with GAT-3, regulates the extracellular GABA levels in the retina, thereby determining the level of inhibitory interactions and affecting visual processing in the retinal pathways. GAT-1 may interact with GABAC receptors on bipolar cell terminals and influence ganglion cell responses. It may also interact with GABAB receptors in the regulation of retinal waves of spontaneous activity which are known to play critical roles during development of the visual system. Other important functional actions are exerted by GAT-1 through reversed GABA transport. These include GABA release by cholinergic/GABAergic starburst amacrine cells and GABA release during early retinal development

The neuropeptide systems and their potential role in the treatment of mammalian retinal ischemia: a developing story

The multiplicity of peptidergic receptors and of the transduction pathways they activate offers the possibility of important advances in the development of specific drugs for clinical treatment of central nervous system disorders. Among them, retinal ischemia is a common clinical entity and, due to relatively ineffective treatment, remains a common cause of visual impairment and blindness. Ischemia is a primary cause of neuronal death, and it can be considered as a sort of final common pathway in retinal diseases leading to irreversible morphological damage and vision loss. Neuropeptides and their receptors are widely expressed in mammalian retinas, where they exert multifaceted functions both during development and in the mature animal. In particular, in recent years somatostatin and pituitary adenylate cyclase activating peptide have been reported to be highly protective against retinal cell death caused by ischemia, while data on opioid peptides, angiotensin II, and other peptides have also been published. This review provides a rationale for harnessing the peptidergic receptors as a potential target against retinal neuronal damages which occur during ischemic retinopathies

Defeasible RDFS via Rational Closure

In the field of non-monotonic logics, the notion of Rational Closure (RC) is acknowledged as a prominent approach. In recent years, RC has gained even more popularity in the context of Description Logics (DLs), the logic underpinning the semantic web standard ontology language OWL 2, whose main ingredients are classes and roles. In this work, we show how to integrate RC within the triple language RDFS, which together with OWL2 are the two major standard semantic web ontology languages. To do so, we start from $\rho df$, which is the logic behind RDFS, and then extend it to $\rho df_\bot$, allowing to state that two entities are incompatible. Eventually, we propose defeasible $\rho df_\bot$ via a typical RC construction. The main features of our approach are: (i) unlike most other approaches that add an extra non-monotone rule layer on top of monotone RDFS, defeasible $\rho df_\bot$ remains syntactically a triple language and is a simple extension of $\rho df_\bot$ by introducing some new predicate symbols with specific semantics. In particular, any RDFS reasoner/store may handle them as ordinary terms if it does not want to take account for the extra semantics of the new predicate symbols; (ii) the defeasible $\rho df_\bot$ entailment decision procedure is build on top of the $\rho df_\bot$ entailment decision procedure, which in turn is an extension of the one for $\rho df$ via some additional inference rules favouring an potential implementation; and (iii) defeasible $\rho df_\bot$ entailment can be decided in polynomial time.Comment: 47 pages. Preprint versio

Recent advances in cellular and molecular aspects of mammalian retinal ischemia

Retinal ischemia is a common clinical entity and, due to relatively ineffective treatment, remains a common cause of visual impairment and blindness. Generally, ischemic syndromes are initially characterized by low homeostatic responses which, with time, induce injury to the tissue due to cell loss by apoptosis. In this respect, retinal ischemia is a primary cause of neuronal death. It can be considered as a sort of final common pathway in retinal diseases and results in irreversible morphological and functional changes. This review summarizes the recent knowledge on the effects of ischemia in retinal tissue and points out experimental strategies/models performed to gain better comprehension of retinal ischemia diseases. In particular, the nature of the mechanisms leading to neuronal damage (i.e., excess of glutamate release, oxidative stress and inflammation) will be outlined as well as the potential and most intriguing retinoprotective approaches and the possible therapeutic use of naturally occurring molecules such as neuropeptides. There is a general agreement that a better understanding of the fundamental pathophysiology of retinal ischemia will lead to better management and improved clinical outcome. In this respect, to contrast this pathological state, specific pharmacological strategies need to be developed aimed at the many putative cascades generated during ischemia

Physiology and pathology of somatostatin in the mammalian retina: a current view

In the retina, peptidergic signalling participates in multiple circuits of visual information processing. The neuropeptide somatostatin (SRIF) is localised to amacrine cells and, in some instances, in a subset of ganglion cells. The variegated expression patterns of SRIF receptors (sst1-sst5) and the variety of signalling mechanisms activated by retinal SRIF suggest that this peptide may exert multiple actions on retinal neurons and on retinal physiology, although our current understanding reflects a rather complicated picture. SRIF, mostly through sst2, may act as a positive factor in the retina by regulating retinal homeostasis and protecting neurons against damage. In this respect, SRIF analogues seem to constitute a promising therapeutic arsenal to cure different retinal diseases, as for instance ischemic and diabetic retinopathies. However, further investigations are needed not only to fully understand the functional role of the SRIF system in the retina but also to exploit new chemical space for drug-like molecules.L'articolo è disponibile sul sito dell'editore http://www.sciencedirect.com

Simple Conditionals with Constrained Right Weakening

In this paper we introduce and investigate a very basic semantics for conditionals that can be used to define a broad class of conditional reasoning systems. We show that it encompasses the most popular kinds of conditional reasoning developed in logic-based KR. It turns out that the semantics we propose is appropriate for a structural analysis of those conditionals that do not satisfy the property of Right Weakening. We show that it can be used for the further development of an analysis of the notion of relevance in conditional reasoning

A polynomial Time Subsumption Algorithm for Nominal Safe ELO under Rational Closure

Description Logics (DLs) under Rational Closure (RC) is a well-known framework for non-monotonic reasoning in DLs. In this paper, we address the concept subsumption decision problem under RC for nominal safe ELO⊥, a notable and practically important DL representative of the OWL 2 profile OWL 2 EL. Our contribution here is to define a polynomial time subsumption procedure for nominal safe ELO⊥ under RC that relies entirely on a series of classical, monotonic EL⊥ subsumption tests. Therefore, any existing classical monotonic EL⊥ reasoner can be used as a black box to implement our method. We then also adapt the method to one of the known extensions of RC for DLs, namely Defeasible Inheritance-based DLs without losing the computational tractability