Probabilities, causation, and logic programming in conditional reasoning: reply to Stenning and Van Lambalgen (2016)

Oaksford and Chater (2014, Thinking and Reasoning, 20, 269–295) critiqued the logic programming (LP) approach to nonmonotonicity and proposed that a Bayesian probabilistic approach to conditional reasoning provided a more empirically adequate theory. The current paper is a reply to Stenning and van Lambalgen's rejoinder to this earlier paper entitled ‘Logic programming, probability, and two-system accounts of reasoning: a rejoinder to Oaksford and Chater’ (2016) in Thinking and Reasoning. It is argued that causation is basic in human cognition and that explaining how abnormality lists are created in LP requires causal models. Each specific rejoinder to the original critique is then addressed. While many areas of agreement are identified, with respect to the key differences, it is concluded the current evidence favours the Bayesian approach, at least for the moment

How to Win First-Order Safety Games

First-order (FO) transition systems have recently attracted attention for the verification of parametric systems such as network protocols, software-defined networks or multi-agent workflows like conference management systems. Functional correctness or noninterference of these systems have conveniently been formulated as safety or hypersafety properties, respectively. In this article, we take the step from verification to synthesis---tackling the question whether it is possible to automatically synthesize predicates to enforce safety or hypersafety properties like noninterference. For that, we generalize FO transition systems to FO safety games. For FO games with monadic predicates only, we provide a complete classification into decidable and undecidable cases. For games with non-monadic predicates, we concentrate on universal first-order invariants, since these are sufficient to express a large class of properties---for example noninterference. We identify a non-trivial sub-class where invariants can be proven inductive and FO winning strategies be effectively constructed. We also show how the extraction of weakest FO winning strategies can be reduced to SO quantifier elimination itself. We demonstrate the usefulness of our approach by automatically synthesizing nontrivial FO specifications of messages in a leader election protocol as well as for paper assignment in a conference management system to exclude unappreciated disclosure of reports

Polynomially bounded forgetting

Forgetting is one of the most important concepts in logic based problem solving, both from a theoretical and a practical point of view. However, the size of the forgetting result is exponential in worst case. To address this issue, we consider the problem of polynomially bounded forgetting, i.e., when the size of the forgetting result can be expressed polynomially.We coin the notion of polynomially bounded forgetting and distinguish several different levels. We then show that forgetting a set of variables under a polynomial bound can be reduced to forgetting a single one. However, checking variable polynomially bounded forgetting is ΣP 2 complete. Hence, we identify some sufficient conditions for this problem. Finally, we consider polynomially bounded forgetting in CNF formulas

How can reasoners simplify database querying (and why haven’t they done it yet)?

The last few decades have seen vast progress in computational reasoning. This has included significant developments in theory, increasing maturity of tools both in performance and usability, and the evolution of standards and benchmarks. The purpose of this article is to reflect on the use of reasoning for rewriting and simplifying relational database queries. We undertake a review of some of the results and reasoning algorithms that have been developed with a motivation from query evaluation, and add to this a look at open problems in the area as well as a critique of prior work from the point of view of practice