Anthia Solaki

Logics for belief as spin-offs of normal modal logics are susceptible to criticisms regarding their potential to model human reasoning, especially in light of empirical evidence on people’s performance in reasoning tasks. The agents are modelled as unlimited reasoners, who perform deductive inferences, introspect, and reason about others’ reasoning, despite bounds of memory or time. To amend this, we propose a hyperintensional doxastic logic for reasoning in a multi-agent setting, which is better aligned with facts on human cognition. We introduce (i) a resource-sensitive impossible-worlds semantics, to account for the fallibility of real reasoners, and (ii) dynamic operators and model updates, inspired by Dynamic Epistemic Logic (DEL), to represent actions that, when affordable, can refine the zero- or higher- order beliefs of agents. The resulting system is applied to case-studies of multi-agent reasoning scenarios. It is thus argued that the framework does justice to non-idealized agents and that it does so in a uniform way, i.e. applicable to both deductive and higher-order reasoning, and in a balanced way, i.e. avoiding criticisms often fired against similar attempts. We finally illustrate a technical connection between this and syntactic approaches against the problem of logical omniscience; this allows us to exploit DEL techniques in obtaining a sound and complete axiomatization.

Theory of Mind (ToM), the cognitive capacity to attribute internal mental states to oneself and others, is a crucial component of social skills. Its formal study has become important, witness recent research on reasoning and information update by intelligent agents, and some proposals for its formal modelling have put forward settings based on Epistemic Logic (EL). Still, due to intrinsic idealisations, it is questionable whether EL can be used to model the high-order cognition of ‘real’ agents. This manuscript proposes a framework that takes visibility, memory, perspective and communication as the main factors underpinning mental attributions. This is more in-line with findings in cognitive science and allows us to model well-known False-Belief Tasks that are typically used in testing people's ToM. We discuss some of the framework's technical features, arguing why it does justice to empirical observations.

In this paper we design a new logical system to explicitly model the different deductive reasoning steps of a boundedly rational agent. We present an adequate system in line with experimental findings about an agent’s reasoning limitations and the cognitive effort that is involved. Inspired by Dynamic Epistemic Logic, we work with dynamic operators denoting explicit applications of inference rules in our logical language. Our models are supplemented by (a) impossible worlds (not closed under logical consequence), suitably structured according to the effect of inference rules, and (b) quantitative components capturing the agent’s cognitive capacity and the cognitive costs of rules with respect to certain resources (e.g. memory, time). These ingredients allow us to avoid problematic logical closure principles, while at the same time deductive reasoning is reflected in our dynamic truth clauses. We further show that our models can be reduced to awareness-like plausibility structures that validate the same formulas and we give a sound and complete axiomatization with respect to them. This approach to the agent’s internal deductive reasoning is finally combined with actions of external information.

We present a framework for epistemic logic, modeling the logical aspects of System 1 and System 2 cognitive processes, as per dual process theories of reasoning. The framework combines non-normal worlds semantics with the techniques of Dynamic Epistemic Logic. It models non-logically-omniscient, but moderately rational agents: their System 1 makes fast sense of incoming information by integrating it on the basis of their background knowledge and beliefs. Their System 2 allows them to slowly, step-wise unpack some of the logical consequences of such knowledge and beliefs, by paying a cognitive cost. The framework is applied to three instances of limited rationality, widely discussed in cognitive psychology: Stereotypical Thinking, the Framing Effect, and the Anchoring Effect.