A Term Logic of Justification for Epistemic Attitudes Fabien Schang Introduction: Term vs Modal Logic Agents are used to thinking. A thought is expressed by a proposition, and thinking consists in a set of related propositions that are taken to be true (accepted) or false (rejected) by the agent. A possible world is such a set of such data (a consistent representation of how the world is), and those data are made of objects and properties; now not every property is considered by an arbitrary agent, due to its limited data. For example, Socrates could not think that Joe Biden would win the 2020 US elections. So if Joe Biden does not belong to the set of objects considered by Socrates, then any proposition about Biden is neither true nor false of Socrates’ thoughts. It might be objected that it is the case that Joe Biden won the 2020 US elections, whatever Socrates may be able to think about it. However, what is said of Socrates in these lines matches with what Sommers [16] calls spanning : a property is said to span an object if, and only if, it makes sense (i.e. it is not absurd) to predicate it of that object. For example, the property of being odd spans the number 2 because it is not absurd (albeit false) to say of 2 that it is odd; whereas being odd does not span Socrates, because it is absurd to assign an algebraic property to a human being. In other words, there is no model where arithmetic properties span individual objects and, if so, not anything can be truly of falsely predicated of a given object. Semantic relevance is mentioned hereby to delimit the set of properties that are to be assigned to objects, accordingly. The same holds for epistemic agents, in the sense that not every proposition is taken to span their thoughts. That is, no epistemic