Probabilistic interpretations of argumentative attacks: logical and experimental foundations

We present an interdisciplinary approach to study systematic relations between logical form and attacks between claims in an argumentative framework. We propose to generalize qualitative attack principles by quantitative ones. Specifically, we use coherent conditional probabilities to evaluate the rationality of principles which govern the strength of argumentative attacks. Finally, we present an experiment which explores the psychological plausibility of selected attack principles

On the Expressivity and Applicability of Model Representation Formalisms

A number of first-order calculi employ an explicit model representation formalism for automated reasoning and for detecting satisfiability. Many of these formalisms can represent infinite Herbrand models. The first-order fragment of monadic, shallow, linear, Horn (MSLH) clauses, is such a formalism used in the approximation refinement calculus. Our first result is a finite model property for MSLH clause sets. Therefore, MSLH clause sets cannot represent models of clause sets with inherently infinite models. Through a translation to tree automata, we further show that this limitation also applies to the linear fragments of implicit generalizations, which is the formalism used in the model-evolution calculus, to atoms with disequality constraints, the formalisms used in the non-redundant clause learning calculus (NRCL), and to atoms with membership constraints, a formalism used for example in decision procedures for algebraic data types. Although these formalisms cannot represent models of clause sets with inherently infinite models, through an additional approximation step they can. This is our second main result. For clause sets including the definition of an equivalence relation with the help of an additional, novel approximation, called reflexive relation splitting, the approximation refinement calculus can automatically show satisfiability through the MSLH clause set formalism.Comment: 15 page

New results on rewrite-based satisfiability procedures

Program analysis and verification require decision procedures to reason on theories of data structures. Many problems can be reduced to the satisfiability of sets of ground literals in theory T. If a sound and complete inference system for first-order logic is guaranteed to terminate on T-satisfiability problems, any theorem-proving strategy with that system and a fair search plan is a T-satisfiability procedure. We prove termination of a rewrite-based first-order engine on the theories of records, integer offsets, integer offsets modulo and lists. We give a modularity theorem stating sufficient conditions for termination on a combinations of theories, given termination on each. The above theories, as well as others, satisfy these conditions. We introduce several sets of benchmarks on these theories and their combinations, including both parametric synthetic benchmarks to test scalability, and real-world problems to test performances on huge sets of literals. We compare the rewrite-based theorem prover E with the validity checkers CVC and CVC Lite. Contrary to the folklore that a general-purpose prover cannot compete with reasoners with built-in theories, the experiments are overall favorable to the theorem prover, showing that not only the rewriting approach is elegant and conceptually simple, but has important practical implications.Comment: To appear in the ACM Transactions on Computational Logic, 49 page

Anomalous visual experience is linked to perceptual uncertainty and visual imagery vividness

An imbalance between top-down and bottom-up processing on perception (specifically, over-reliance on top-down processing) can lead to anomalous perception, such as illusions. One factor that may be involved in anomalous perception is visual mental imagery, which is the experience of “seeing” with the mind’s eye. There are vast individual differences in self-reported imagery vividness, and more vivid imagery is linked to a more sensory-like experience. We, therefore, hypothesized that susceptibility to anomalous perception is linked to individual imagery vividness. To investigate this, we adopted a paradigm that is known to elicit the perception of faces in pure visual noise (pareidolia). In four experiments, we explored how imagery vividness contributes to this experience under different response instructions and environments. We found strong evidence that people with more vivid imagery were more likely to see faces in the noise, although removing suggestive instructions weakened this relationship. Analyses from the first two experiments led us to explore confidence as another factor in pareidolia proneness. We, therefore, modulated environment noise and added a confidence rating in a novel design. We found strong evidence that pareidolia proneness is correlated with uncertainty about real percepts. Decreasing perceptual ambiguity abolished the relationship between pareidolia proneness and both imagery vividness and confidence. The results cannot be explained by incidental face-like patterns in the noise, individual variations in response bias, perceptual sensitivity, subjective perceptual thresholds, viewing distance, testing environments, motivation, gender, or prosopagnosia. This indicates a critical role of mental imagery vividness and perceptual uncertainty in anomalous perceptual experience. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (10.1007/s00426-020-01364-7) contains supplementary material, which is available to authorized users

On the Expressivity and Applicability of Model Representation Formalisms

International audienceA number of first-order calculi employ an explicit model representation formalism in support of non-redundant inferences and for detecting satisfiability. Many of these formalisms can represent infinite Herbrand models. The first-order fragment of monadic, shallow, linear, Horn (MSLH) clauses, is such a formalism used in the approximation refinement calculus (AR). Our first result is a finite model property for MSLH clause sets. Therefore, MSLH clause sets cannot represent models of clause sets with inherently infinite models. Through a translation to tree automata, we further show that this limitation also applies to the linear fragments of implicit generalizations, which is the formalism used in the model-evolution calculus (ME), to atoms with disequality constraints, the formalisms used in the non-redundant clause learning calculus (NRCL), and to atoms with membership constraints, a formalism used for example in decision procedures for algebraic data types. Although these formalisms cannot represent models of clause sets with inherently infinite models, through an additional approximation step they can. This is our second main result. For clause sets including the definition of an equivalence relation with the help of an additional, novel approximation, called reflexive relation splitting, the approximation refinement calculus can automatically show satisfiability through the MSLH clause set formalism