By extending the quantifier-free predicate logic (without equality, constant and function symbols) with a bundled modality ∃ x , which packs the quantifier ∃ x and the modality together, we obtain a fragment of first-order modal logic, namely, ∃ -bundled fragment. In this paper, we prove that the Craig interpolation theorem holds for systems of the ∃ -bundled fragment based on K/D/T/4/S4, while it fails for the system based on S5.
We show how techniques from Belief Revision Theory and Dynamic Epistemic Logic can solve the Surprise Examination Paradox. Our solution is based on formalizing the role played by the attitude of the Student towards the Teacher as a source of information.
This paper explores the effect of social structures on the beliefs and knowledge of agents who reason in an evidence-based manner. We introduce Evidence Diffusion Models for the formal analysis of multi-agent evidence-based reasoning, focusing on the context of a social network where evidence pieces are being communicated between agents via threshold-limited diffusion. Our models bridge the gap between multi-agent Topological Evidence Models (Partitional Models) and Threshold Models for Diffusion. Firstly, we show that, in our setting, network structures are expressible and known both defeasibly and infallibly by the agents. Then, we prove that defeasible knowledge and (defeasible) 'evidence-based distributed knowledge' are easily lost under the diffusion of pieces of evidence in a network, whereas 'group knowledge with distributed evidence' is strongly robust. Finally, we obtain so-called Cluster Theorems characterising the evidential and network conditions for evidence cascades to form, and for individuals and groups to obtain knowledge in the diffusion process.
Disjunctive reasoning, or reasoning by cases, plays a central role in defeasible frameworks and normative systems. This paper adopts a cautious approach, suggesting that rebutting disjunctive paths may render the inference defeasible, particularly in the context of default-based reasoning. To formalize this, we introduce explicit hypotheses to track reasoning paths. Building on prior work, we refine a class of Argument Calculi into a robust method for disjunctive reasoning in nonmonotonic logics, for both normative and doxastic interpretations of our system. We propose meta-theoretical properties tailored to disjunctive reasoning: disjunctive consistency and hypothetical consistency, which constrain argument behavior involving disjunction. By systematically comparing Argument Calculi against several properties, we analyze their implications for consistency and nonmonotonic inference in default-based frameworks.
Causal models consisting of structural equations have proved a powerful formalism for approaching theoretical and applied questions on causal reasoning. The standard framework assumes that all variables that appear in a causal model must represent properties or events that are metaphysically independent, with no dependencies more intimate than causal relations, such as conceptual, constitutive, or other ontological dependencies. However, there are important contexts that call for lifting this restriction, such as the debate over high-level causation in philosophy and the task of causal representation learning in artificial intelligence. This paper proposes a natural generalization of structural causal models to accommodate (asymmetric) ontological dependence and provides an interpretation of causal counterfactuals based on such models. We discuss several implications of this generalization and present an axiomatization of the resulting counterfactual logic.
