Human language is used to express logical and mathematical computations whose cognitive bases still remain unexplained. We ask ourselves if language acquisition involves a kind of implicit logical and mathematical programming that could explain such performances. Examples of these performances are some logical propositions, transferred by natural language, valid for different languages and for large populations of humans sharing similar cultural traditions. In the present work we choose -as a largely accepted logical statement-one of the most cited expressions that Arthur Conan Doyle attributed to Sherlock Holmes, the "old maxim" mentioned by the character in the story "The Adventure of the Beryl Coronet". For an allusion to this maxim in a scientific context see Cairns-Smith (1990).

The rich expressivity provided by the cognitive event calculus (CEC) knowledge representation framework allows for reasoning over deeply nested beliefs, desires, intentions, and so on. I put CEC to the test by attempting to model the complex reasoning and deceptive planning used in an episode of the popular television show Breaking Bad. CEC is used to represent the knowledge used by reasoners coming up with plans like the ones devised by the fictional characters I describe. However, it becomes clear that a form of nonmonotonic reasoning is necessary—specifically so that an agent can reason about the nonmonotonic beliefs of another agent. I show how CEC can be augmented to have this ability, and then provide examples detailing how my proposed augmentation enables much of the reasoning used by agents such as the Breaking Bad characters. I close by discussing what sort of reasoning tool would be necessary to implement such nonmonotonic reasoning.

Believability requires video game characters to consider their actions within the context of social norms. Social norms involve a broad range of behavioral defaults, obligations, and injunctions unrelated to strictly causal reasoning.  Defeasible reasoning involves rationally compelling but deductively invalid arguments, such as reasoning with rules that allow exceptions. This paper investigates having video game characters use defeasible reasoning to consider injunctive social norms when selecting and planning actions.

Multi-context Systems (MCSs) are a formalism for systems consisting of knowledge bases (possibly heterogeneous and non-monotonic) that are interlinked via bridge rules, where the global system semantics emerges from the local semantics of the knowledge bases (also called contexts) in an equilibrium. While MCSs and related formalisms are inherently targeted for distributed set- tings, no truly distributed algorithms for their evaluation were available. We address this short- coming and present a suite of such algorithms which includes a basic algorithm DMCS, an ad- vanced version DMCSOPT that exploits topology-based optimizations, and a streaming algorithm DMCS-STREAMING that computes equilibria in packages of bounded size. The algorithms be- have quite differently in several respects, as experienced in thorough experimental evaluation of a system prototype. From the experimental results, we derive a guideline for choosing the appropriate algorithm and running mode in particular situations, determined by the parameter settings.

The theory of (variable) forgetting has received significant attention in nonmonotonic reasoning, especially, in answer set programming. However, the problem of establishing a theory of forgetting for some expressive nonmonotonic logics such as McCarthy's circumscription is rarely explored.In this paper a theory of forgetting for propositional circumscription is proposed, which is not a straightforward adaption of existing approaches. In particular, some properties that are essential for existing proposals do not hold any longer or have to be reformulated. Several useful properties of the new forgetting are proved, which demonstrate suitability of the forgetting for circumscription. A sound and complete algorithm for the forgetting is developed and an analysis of computational complexity is given.

As fragments of first-order logic, Description logics (DLs) do not provide nonmonotonic features such as defeasible inheritance and default rules. Since many applications would benefit from the availability of such features, several families of nonmonotonic DLs have been developed that are mostly based on default logic and autoepistemic logic. In this paper, we consider circumscription as an interesting alternative approach to nonmonotonic DLs that, in particular, supports defeasible inheritance in a natural way. We study DLs extended with circumscription under different language restrictions and under different constraints on the sets of minimized, fixed, and varying predicates, and pinpoint the exact computational complexity of reasoning for DLs ranging from ALC to ALCIO and ALCQO. When the minimized and fixed predicates include only concept names but no role names, then reasoning is complete for NExpTime^NP. It becomes complete for NP^NExpTime when the number of minimized and fixed predicates is bounded by a constant. If roles can be minimized or fixed, then complexity ranges from NExpTime^NP to undecidability.

Since it is a relatively new concept, little is known about the computational complexity of fuzzy answer set programming (FASP) and almost no techniques are available to compute answer sets of FASP programs. Furthermore, the connections of FASP to other paradigms of nonmonotonic reasoning with continuous values are largely unexplored. In our disertation, we contribute to the ongoing research on FASP on two different levels: complexity and connections to fuzzy modal logics.

A notion of quantified conditional logics is provided that includes quantification over individual and propositional variables. The former is supported with respect to constant and variable domain semantics. In addition, a sound and complete embedding of this framework in classical higher-order logic is presented. Using prominent examples from the literature it is demonstrated how this embedding enables effective automation of reasoning within (object-level) and about (meta-level) quantified conditional logics with off-the-shelf higher-order theorem provers and model finders.

(l) I have enough evidence to render the sentence S probable. (la) So, relative to what I know, it is rational of me to believe S. (2) Now that I have more evidence, S may no longer be probable. (2a) So now, relative to what I know, it is not rational of me to believe S. These seem a perfectly ordinary, common sense, pair of situations. Generally and vaguely, I take them to embody what I shall call probabilistic inference. This form of inference is clearly non-monotonic. Relatively few people have taken this form of inference, based on high probability, to serve as a foundation for non-monotonic logic or for a logical or defeasible inference. There are exceptions: Jane Nutter [16] thinks that sometimes probability has something to do with non-monotonic reasoning. Judea Pearl [ 17] has recently been exploring the possibility. There are any number of people whom one might call probability enthusiasts who feel that probability provides all the answers by itself, with no need of help from logic. Cheeseman [1], Henrion [5] and others think it useful to look at a distribution of probabilities over a whole algebra of statements, to update that distribution in the light of new evidence, and to use the latest updated distribution of probability over the algebra as a basis for planning and decision making. A slightly weaker form of this approach is captured by Nilsson [15], where one assumes certain probabilities for certain statements, and infers the probabilities, or constraints on the probabilities of other statement. None of this corresponds to what I call probabilistic inference. All of the inference that is taking place, either in Bayesian updating, or in probabilistic logic, is strictly deductive. Deductive inference, particularly that concerned with the distribution of classical probabilities or chances, is of great importance. But this is not to say that there is no important role for what earlier logicians have called "ampliative" or "inductive" or "scientific" inference, in which the conclusion goes beyond the premises, asserts more than do the premises. This depends on what David Israel [6] has called "real rules of inference". It is characteristic of any such logic or inference procedure that it can go wrong: that statements accepted at one point may be rejected at a later point. Research underlying the results reported here has been partially supported by the Signals Warfare Center of the United States Army.

This note is concerned with a formal analysis of the problem of nonmonotonic reasoning in intelligent systems, especially when the uncertainty is taken into account in a quantitative way. A firm connection between logic and probability is established by introducing conditioning notions by means of formal structures that do not rely on quantitative measures. The associated conditional logic, compatible with conditional probability evaluations, is nonmonotonic relative to additional evidence. Computational aspects of conditional probability logic are mentioned. The importance of this development lies on its role to provide a conceptual basis for various forms of evidence combination and on its significance to unify multi-valued and nonmonotonic logics. Introduction Consider the case of automated reasoning under uncertainty in which we wish to take into account the uncertainty in a quantitative way.