Abstract: Formal approaches that aim at representing human reasoning should be evaluated based on how humans actually reason. One way in doing so, is to investigate whether psychological findings of human reasoning patterns are represented in the theoretical model. The computational logic approach discussed here is the so called weak completion semantics which is based on the three-valued Lukasiewicz logic. We explain how this approach adequately models Byrne's suppression task, a psychological study where the experimental results show that participants' conclusions systematically deviate from the classical logically correct answers. As weak completion semantics is a novel technique in the field of Computational Logic, it is important to examine how it corresponds to other already established non-monotonic approaches. For this purpose we investigate the relation of weak completion with respect to completion and three-valued stable model semantics. In particular, we show that well-founded semantics, a widely accepted approach in the field of non-monotonic reasoning, corresponds to weak completion semantics for a specific class of modified programs.

The belief bias effect is a phenomenon which occurs when we think that we judge an argument based on our reasoning, but are actually influenced by our beliefs and prior knowledge. Evans, Barston and Pollard carried out a psychological syllogistic reasoning task to prove this effect. Participants were asked whether they would accept or reject a given syllogism. We discuss one specific case which is commonly assumed to be believable but which is actually not logically valid. By introducing abnormalities, abduction and background knowledge, we adequately model this case under the weak completion semantics. Our formalization reveals new questions about possible extensions in abductive reasoning. For instance, observations and their explanations might include some relevant prior abductive contextual information concerning some side-effect or leading to a contestable or refutable side-effect. A weaker notion indicates the support of some relevant consequences by a prior abductive context. Yet another definition describes jointly supported relevant consequences, which captures the idea of two observations containing mutually supportive side-effects. Though motivated with and exemplified by the running psychology application, the various new general abductive context definitions are introduced here and given a declarative semantics for the first time, and have a much wider scope of application. Inspection points, a concept introduced by Pereira and Pinto, allows us to express these definitions syntactically and intertwine them into an operational semantics.

We construct a counterfactual statement when we reason conjecturally about an event which did or did not occur in the past: If an event had occurred, what would have happened? Would it be relevant? Real world examples, as stud-ied by Byrne, Rescher and many others, show that these conditionals involve a complex reasoning process. An intuitive and elegant approach to evaluate counterfactuals, without deep revision mechanisms, is proposed by Pearl. His Do-Calculus identifies causal relations in a Bayesian network resorting to coun-terfactuals. Though leaving out probabilities, we adopt Pearl’s stance, and its prior epistemological justification to counterfactuals in causal Bayesian net-works, but for programs. Logic programming seems a suitable environment for several reasons. First, its inferential arrow is adept at expressing causal direc-tion and conditional reasoning. Secondly, together with its other functionalities such as abduction, integrity constraints, revision, updating and debugging (a form of counterfactual reasoning), it proffers a wide range of expressibility it-self. We show here how programs under the weak completion semantics in an abductive framework, comprising the integrity constraints, can smoothly and uniformly capture well-known and off-the-shelf counterfactual problems and conundrums, taken from the psychological and philosophical literature. Our approach is adroitly reconstructable in other three-valued LP semantics, or re-stricted to two-valued ones.

We discuss the evaluation of conditionals. Under classical logic a conditional of the form A implies B is semantically equivalent to not A or B. However, psychological experiments have repeatedly shown reduction system under the three-valued Lukasiewicz logic and the weak completion semantics, that allows us to reason abductively and by revision with respect to conditionals, in three values. We discuss the strategy of minimal revision followed by abduction and discuss two notions of relevance. Psychological experiments will need to ascertain if these strategies and notions, or a variant of them, correspond to how humans reason with conditionals. 1

Stenning and van Lambalgen introduced an approach to model empirically studied human reasoning with nonmonotonic logics. Some of the research questions that have been brought up in this context concern the interplay of the open- and closed-world assumption, the suitability of particular logic programming semantics for the modeling of human reasoning, and the role of three-valued logic programming semantics and three-valued logics. We look into these questions from the view of a framework where logic programs that model human reasoning are represented declaratively and are mechanizable by classical formulas extended with certain second-order operators.

submitted; revised; accepted Abduction has been on the back burner in logic programming, as abduction can be too difficult to implement, and costly to perform, in particular if abductive solutions are not tabled for reuse. On the other hand, current Prolog systems, with their tabling mechanisms, are mature enough to facilitate the specific introduction of tabling abductive solutions (tabled abduction) into them. Our contributions are as follows: (1) We conceptualize tabled abduction for abductive normal logic programs, permitting abductive solutions to be reused, from one abductive context to another. The approach relies on a transformation into tabled logic programs that makes use of the dual transformation, and enables efficiently handling the problem of abduction under negative goals, by introducing dual positive counterparts for them. (2) We realize tabled abduction in Tabdual, a system implemented in XSB Prolog, allowing dualization by-need only. (3) We refine the dual transformation in the context of Tabdual to permit executing programs with variables and non-ground queries. (4) We foster pragmatic approaches in Tabdual to cater to all varieties of loops in normal logic programs, now complicated by abduction. (5) We evaluate Tabdual in practice by examining five variants, according to various evaluation objectives. (6) We detail how Tabdual can be applied to declarative debugging and decision making. (7) Finally, we refer to related work, and discuss Tabdual’s correctness, complexity, and features that could migrate to the engine level, in Logic Programming systems wanting to encompass tabled abduction. Eight appendices complement and detail the main text.

Abstract In this paper we present a new approach to evaluate indicative conditionals with respect to some background information specified by a logic program. Because the weak completion of a logic program admits a least model under the three-valued Lukasiewicz semantics and this semantics has been successfully applied to other human reasoning tasks, conditionals are evaluated under these least L-models. If such a model maps the condition of a conditional to unknown, then abduction and revision are applied in order to satisfy the condition. Different strategies in applying abduction and revision might lead to different evaluations of a given conditional. Based on these findings we outline an experiment to better understand how humans handle those cases. 1 Indicative Conditionals Conditionals are statements of the form if condition then consequence. In the literature the condition is also called if part, if clause or protasis, whereas the consequence is called then part, then clause or apodosis. Conditions as well as

The tendency to accept or reject arguments based on own beliefs or prior knowledge rather than on the rea-soning process is called the belief-bias effect. A psy-chological syllogistic reasoning task shows this phe-nomenon, wherein participants were asked whether they accept or reject a given syllogism. We discuss one case which is commonly assumed to be believable but not logically valid. By introducing abnormalities, abduction and background knowledge, we model this case under the weak completion semantics. Our formalization re-veals new questions about observations and their ex-planations which might include some relevant prior ab-ductive contextual information concerning some side-effect. Inspection points, introduced by Pereira and Pinto, allow us to express these definitions syntactically and intertwine them into an operational semantics.

Abstract. In this paper we discuss conjunctive planning problems in the context of the fluent calculus and Petri nets. We show that both formalisms are equivalent in solving these problems. Thereafter, we ex-tend actions to contain preconditions as well as obstacles. This requires to extend the fluent calculus as well as Petri nets. Again, we show that both extended formalisms are equivalent. 1

Fluent Calculus ’ and the work presented in it are my own. I confirm that: This work was done wholly or mainly while in candidature for a research degree at Technische Universität Dresden. Where any part of this thesis has previously been submitted for a degree or any other qualification at Technische Universität Dresden or any other institution, this has been clearly stated. Where I have consulted the published work of others, this is always clearly attributed. Where I have quoted from the work of others, the source is always given. With the exception of such quotations, this thesis is entirely my own work. I have acknowledged all main sources of help. Where the thesis is based on work done by myself jointly with others, I have made clear exactly what was done by others and what I have contributed myself.