On the Completeness of Spider Diagrams Augmented with Constants

Diagrammatic reasoning can be described formally by a number of diagrammatic logics; spider diagrams are one of these, and are used for expressing logical statements about set membership and containment. Here, existing work on spider diagrams is extended to include constant spiders that represent specific individuals. We give a formal syntax and semantics for the extended diagram language before introducing a collection of reasoning rules encapsulating logical equivalence and logical consequence. We prove that the resulting logic is sound, complete and decidable

Step-Indexed Logical Relations for Probability (long version)

It is well-known that constructing models of higher-order probabilistic programming languages is challenging. We show how to construct step-indexed logical relations for a probabilistic extension of a higher-order programming language with impredicative polymorphism and recursive types. We show that the resulting logical relation is sound and complete with respect to the contextual preorder and, moreover, that it is convenient for reasoning about concrete program equivalences. Finally, we extend the language with dynamically allocated first-order references and show how to extend the logical relation to this language. We show that the resulting relation remains useful for reasoning about examples involving both state and probabilistic choice.Comment: Extended version with appendix of a FoSSaCS'15 pape

A Framework for Combining Defeasible Argumentation with Labeled Deduction

In the last years, there has been an increasing demand of a variety of logical systems, prompted mostly by applications of logic in AI and other related areas. Labeled Deductive Systems (LDS) were developed as a flexible methodology to formalize such a kind of complex logical systems. Defeasible argumentation has proven to be a successful approach to formalizing commonsense reasoning, encompassing many other alternative formalisms for defeasible reasoning. Argument-based frameworks share some common notions (such as the concept of argument, defeater, etc.) along with a number of particular features which make it difficult to compare them with each other from a logical viewpoint. This paper introduces LDSar, a LDS for defeasible argumentation in which many important issues concerning defeasible argumentation are captured within a unified logical framework. We also discuss some logical properties and extensions that emerge from the proposed framework.Comment: 15 pages, presented at CMSRA Workshop 2003. Buenos Aires, Argentin

Combining logic and probability in tracking and scene interpretation

The paper gives a high-level overview of some ways in which logical representations and reasoning can be used in computer vision applications, such as tracking and scene interpretation. The combination of logical and statistical approaches is also considered

Logical reasoning in schizotypal personality

It was examined whether psychotic-like personality traits in a sample of 205 college students could predict logical reasoning deficits, akin to those seen in schizophrenia. The participants were tested on their ability to assess the logical validity of premises (Logical Reasoning Task), and completed a multi-dimensional schizotypy inventory (O-LIFE). Low accuracy was associated with increased levels of disorganized schizotypy (‘Cognitive Disorganization’), while elevated errors were associated with increased levels of positive (‘Unusual Experiences’), negative (‘Introvertive Anhedonia’) and impulsive (‘Impulsivity Non-conformity’) schizotypy. Nevertheless, multiple regression analyses revealed that negative schizotypy was retained as the only significant predictor after performance was corrected for random guessing, and the contribution of the average amount of time spent on each premise was controlled. The results suggest that, although most schizotypy dimensions have a detrimental effect on reasoning performance, possibly due to disadvantageous test-taking strategies, negative schizotypy is the most reliable predictor of logical reasoning deficits. It is proposed that social/interpersonal schizotypal traits, like negative symptoms of schizophrenia, are accompanied by deficient executive functions of working memory, which appear to undermine, inter alia, logical reasoning processing