Resource-origins of Nonmonotonicity

Formal nonmonotonic systems try to model the phenomenon that common sense reasoners are able to “jump” in their reasoning from assumptions Δ to conclusions C without their being any deductive chain from Δ to C. Such jumps are done by various mechanisms which are strongly dependent on context and knowledge of how the actual world functions. Our aim is to motivate these jump rules as inference rules designed to optimise survival in an environment with scant resources of effort and time. We begin with a general discussion and quickly move to Section 3 where we introduce five resource principles. We show that these principles lead to some well known nonmonotonic systems such as Nute’s defeasible logic. We also give several examples of practical reasoning situations to illustrate our principles. Edited by Hannes Leitgeb     

The soft embodiment of culture: camera angles and motion through time and space

Cultural assumptions about one's relation to others and one's place in the world can be literally embodied in the way one cognitively maps out one's position and motion in time and space. In three experiments, we examined the psychological perspective that Asian American and Euro-American participants embodied as they both comprehended and produced narratives and mapped out metaphors of time and space. In social situations, Euro-American participants were more likely to embody their own perspective and a sense of their own motion (rather than those of a friend), whereas Asian American participants were more likely to embody a friend's perspective and sense of motion (rather than their own). We discuss how these psychological perspectives represent the soft embodiment of culture by implicitly instantiating cultural injunctions (a) to think about how you look to others and to harmonize with them or (b) to know yourself, trust yourself, and act with confidence.     

Complete Extensions in Argumentation Coincide with 3-Valued Stable Models in Logic Programming

In this paper, we prove the correspondence between complete extensions in abstract argumentation and 3-valued stable models in logic programming. This result is in line with earlier work of [6] that identified the correspondence between the grounded extension in abstract argumentation and the well-founded model in logic programming, as well as between the stable extensions in abstract argumentation and the stable models in logic programming.     

Meta-Argumentation Modelling I: Methodology and Techniques

In this paper, we introduce the methodology and techniques of meta-argumentation to model argumentation. The methodology of meta-argumentation instantiates Dung’s abstract argumentation theory with an extended argumentation theory, and is thus based on a combination of the methodology of instantiating abstract arguments, and the methodology of extending Dung’s basic argumentation frameworks with other relations among abstract arguments. The technique of meta-argumentation applies Dung’s theory of abstract argumentation to itself, by instantiating Dung’s abstract arguments with meta-arguments using a technique called flattening. We characterize the domain of instantiation using a representation technique based on soundness and completeness. Finally, we distinguish among various instantiations using the technique of specification languages.     

Modal Logics of Reactive Frames

A reactive graph generalizes the concept of a graph by making it dynamic, in the sense that the arrows coming out from a point depend on how we got there. This idea was first applied to Kripke semantics of modal logic in [2]. In this paper we strengthen that unimodal language by adding a second operator. One operator corresponds to the dynamics relation and the other one relates paths with the same endpoint. We explore the expressivity of this interpretation by axiomatizing some natural subclasses of reactive frames. The main objective of this paper is to present a methodology to study reactive logics using the existent classic techniques.     

Logical Modes of Attack in Argumentation Networks

This paper studies methodologically robust options for giving logical contents to nodes in abstract argumentation networks. It defines a variety of notions of attack in terms of the logical contents of the nodes in a network. General properties of logics are refined both in the object level and in the metalevel to suit the needs of the application. The network-based system improves upon some of the attempts in the literature to define attacks in terms of defeasible proofs, the so-called rule-based systems. We also provide a number of examples and consider a rigorous case study, which indicate that our system does not suffer from anomalies. We define consequence relations based on a notion of defeat, consider rationality postulates, and prove that one such consequence relation is consistent.     

Annotation Theories over Finite Graphs

In the current paper we consider theories with vocabulary containing a number of binary and unary relation symbols. Binary relation symbols represent labeled edges of a graph and unary relations represent unique annotations of the graph’s nodes. Such theories, which we call annotation theories, can be used in many applications, including the formalization of argumentation, approximate reasoning, semantics of logic programs, graph coloring, etc. We address a number of problems related to annotation theories over finite models, including satisfiability, querying problem, specification of preferred models and model checking problem. We show that most of considered problems are NPTime- or co-NPTime-complete. In order to reduce the complexity for particular theories, we use second-order quantifier elimination. To our best knowledge none of existing methods works in the case of annotation theories. We then provide a new second-order quantifier elimination method for stratified theories, which is successful in the considered cases. The new result subsumes many other results, including those of [2, 28, 21].     

Analysis of the Talmudic Argumentum A Fortiori Inference Rule (Kal Vachomer) using Matrix Abduction

We motivate and introduce a new method of abduction, Matrix Abduction, and apply it to modelling the use of non-deductive inferences in the Talmud such as Analogy and the rule of Argumentum A Fortiori. Given a matrix \({\mathbb {A}}\) with entries in {0, 1}, we allow for one or more blank squares in the matrix, say a _i,j =?. The method allows us to decide whether to declare a _i,j = 0 or a _i,j = 1 or a _i,j =? undecided. This algorithmic method is then applied to modelling several legal and practical reasoning situations including the Talmudic rule of Kal-Vachomer. We add an Appendix showing that this new rule of Matrix Abduction, arising from the Talmud, can also be applied to the analysis of paradoxes in voting and judgement aggregation. In fact we have here a general method for executing non-deductive inferences.     

Semantic asymmetries are modulated by phonological asymmetries: Evidence from the disambiguation of homophonic versus heterophonic homographs

The present study investigated cerebral asymmetries in accessing multiple meanings of two types of homographs: homophonic homographs (e.g., bank) and heterophonic homographs (e.g., tear). Participants read homographs preceded by either a biasing or a non-biasing sentential context and performed a lexical decision on lateralized targets presented 150 ms after onset of the sentence-final ambiguous prime. Targets were either related to the dominant or the subordinate meaning of the preceding homograph or were unrelated to it. In the case of homophonic homographs – our results converge with previous findings: both activation and selection processes are faster in the LH than in the RH. Importantly, however, in the case of heterophonic homographs – opposite asymmetries were found. These results suggest that semantic asymmetries are modulated by phonology. They are discussed in the context of a model of functional architecture of reading in the two hemispheres in which orthography, phonology and semantics are fully interconnected in the LH, whereas in the RH, orthography and phonology are not directly connected, such that phonological processes are mediated by semantics.