A review of proposed principles of causal non-monotonic reasoning

Within Non-monotonic Reasoning, numerous principles of causal reasoning have been proposed. Many of these principles have been viewed as desirable in formalisms that reason with causality, and have been widely adopted throughout the literature. We provide a critique of these principles, evaluate their suitability for characterising and formulating causal non-monotonic reasoning, and find that most are unsuitable. Further, we discuss a new approach to causal non-monotonic reasoning motivated by how humans typically reason with causality

A review of proposed principles of causal non-monotonic reasoning

Within Non-monotonic Reasoning, numerous principles of causal reasoning have been proposed. Many of these principles have been viewed as desirable in formalisms that reason with causality, and have been widely adopted throughout the literature. We provide a critique of these principles, evaluate their suitability for characterising and formulating causal non-monotonic reasoning, and find that most are unsuitable. Further, we discuss a new approach to causal non-monotonic reasoning motivated by how humans typically reason with causality

Metatheory of actions: beyond consistency

Consistency check has been the only criterion for theory evaluation in logic-based approaches to reasoning about actions. This work goes beyond that and contributes to the metatheory of actions by investigating what other properties a good domain description in reasoning about actions should have. We state some metatheoretical postulates concerning this sore spot. When all postulates are satisfied together we have a modular action theory. Besides being easier to understand and more elaboration tolerant in McCarthy's sense, modular theories have interesting properties. We point out the problems that arise when the postulates about modularity are violated and propose algorithmic checks that can help the designer of an action theory to overcome them

Counterfactuals as modal conditionals, and their probability

In this paper we propose a semantic analysis of Lewis' counterfactuals. By exploiting the structural properties of the recently introduced boolean algebras of conditionals, we show that counterfactuals can be expressed as formal combinations of a conditional object and a normal necessity modal operator. Specifically, we introduce a class of algebras that serve as modal expansions of boolean algebras of conditionals, together with their dual relational structures. Moreover, we show that Lewis' semantics based on sphere models can be reconstructed in this framework. As a consequence, we establish the soundness and completeness of a slightly stronger variant of Lewis' logic for counterfactuals with respect to our algebraic models. In the second part of the paper, we present a novel approach to the probability of counterfactuals showing that it aligns with the uncertainty degree assigned by a belief function, as per Dempster-Shafer theory, to its associated conditional formula. Furthermore, we characterize the probability of a counterfactual in terms of Gärdenfors' imaging rule for the probabilistic update

Regression in Modal Logic

In this work we propose an encoding of Reiter’s Situation Calculus solution to the frame problem into the framework of a simple multimodal logic of actions. In particular we present the modal counterpart of the regression technique. This gives us a theorem proving method for a relevant fragment of our modal logic