A logic of default justifications

We define a logic of default justifications that relies on operational semantics. One of the key features that is absent in standard justification logics is the possibility to weigh different epistemic reasons or pieces of evidence that might conflict with one another. To amend this inadequacy, we develop a semantics for “defeaters”: conflicting reasons forming a basis to doubt the original conclusion or to believe an opposite statement. Our logic is able to address interactions of normal defaults without relying on priorities among default rules and introduces the possibility of extension revision for normal default theories

A formal analysis of the notion of preference between deductive arguments

In the last two decades, justification logic has addressed the problem of including justifications into the field of epistemic logic. Nevertheless, there is something that has not received enough attention yet: how epistemic agents might prefer certain justifications to others, in order to have better pieces of evidence to support a particular belief. In this work, we study the notion of preference between a particular kind of justifications: deductive arguments. For doing so, we have built a logic using tools from epistemic logic, justification logic and logics for belief dependence. According to our solution, the preferences of an epistemic agent between different deductive arguments can be reduced to other notions

Argument-based Belief in Topological Structures

This paper combines two studies: a topological semantics for epistemic notions and abstract argumentation theory. In our combined setting, we use a topological semantics to represent the structure of an agent's collection of evidence, and we use argumentation theory to single out the relevant sets of evidence through which a notion of beliefs grounded on arguments is defined. We discuss the formal properties of this newly defined notion, providing also a formal language with a matching modality together with a sound and complete axiom system for it. Despite the fact that our agent can combine her evidence in a 'rational' way (captured via the topological structure), argument-based beliefs are not closed under conjunction. This illustrates the difference between an agent's reasoning abilities (i.e. the way she is able to combine her available evidence) and the closure properties of her beliefs. We use this point to argue for why the failure of closure under conjunction of belief should not bear the burden of the failure of rationality.Comment: In Proceedings TARK 2017, arXiv:1707.0825

Logic of Non-Monotonic Interactive Proofs (Formal Theory of Temporary Knowledge Transfer)

We propose a monotonic logic of internalised non-monotonic or instant interactive proofs (LiiP) and reconstruct an existing monotonic logic of internalised monotonic or persistent interactive proofs (LiP) as a minimal conservative extension of LiiP. Instant interactive proofs effect a fragile epistemic impact in their intended communities of peer reviewers that consists in the impermanent induction of the knowledge of their proof goal by means of the knowledge of the proof with the interpreting reviewer: If my peer reviewer knew my proof then she would at least then (in that instant) know that its proof goal is true. Their impact is fragile and their induction of knowledge impermanent in the sense of being the case possibly only at the instant of learning the proof. This accounts for the important possibility of internalising proofs of statements whose truth value can vary, which, as opposed to invariant statements, cannot have persistent proofs. So instant interactive proofs effect a temporary transfer of certain propositional knowledge (knowable ephemeral facts) via the transmission of certain individual knowledge (knowable non-monotonic proofs) in distributed systems of multiple interacting agents.Comment: continuation of arXiv:1201.3667 ; published extended abstract: DOI:10.1007/978-3-642-36039-8_16 ; related to arXiv:1208.591