Related papers: Arrow-Type Impossibility for Genuinely Modal Judgm…
There is an extensive literature in social choice theory studying the consequences of weakening the assumptions of Arrow's Impossibility Theorem. Much of this literature suggests that there is no escape from Arrow-style impossibility…
We analyse the computational complexity of three problems in judgment aggregation: (1) computing a collective judgment from a profile of individual judgments (the winner determination problem); (2) deciding whether a given agent can…
When aggregating logically interconnected judgments from $n$ agents, the result might be inconsistent with the logical connection. This inconsistency is known as the doctrinal paradox, which plays a central role in the field of judgment…
This paper synthesizes a series of formal proofs to construct a unified theory on the logical limits of the Symbol Grounding Problem. We distinguish between internal meaning (sense), which formal systems can possess via axioms, and external…
Recursive relational specifications are commonly used to describe the computational structure of formal systems. Recent research in proof theory has identified two features that facilitate direct, logic-based reasoning about such…
A combinatorial theory of associative $n$-categories has recently been proposed, with strictly associative and unital composition in all dimensions, and the weak structure arising as a combinatorial notion of homotopy with a natural…
A logic has uniform interpolation if its formulas can be projected down to given subsignatures, preserving all logical consequences that do not mention the removed symbols; the weaker property of (Craig) interpolation allows the projected…
In the present paper we consider modal propositional logic and look for the constraints that are imposed to the propositions of the special type $\Box a$ by the structure of the relevant finite Kripke frame. We translate the usual language…
Coalition Logic is primarily concerned with what coalitions can achieve, whereas what coalitions cannot achieve -- their \emph{inability} -- has received comparatively little explicit attention. This asymmetry matters in artificial…
I investigate the modal commitments of various conceptions of the philosophy of arithmetic potentialism. Specifically, I shall consider the potentialist conceptions arising from a model-theoretic view of the models of arithmetic as possible…
In this paper we explore the application of methods for classical judgment aggregation in pooling probabilistic opinions on logically related issues. For this reason, we first modify the Boolean judgment aggregation framework in the way…
The Abstraction and Reasoning Corpus (ARC) provides a compact laboratory for studying abstract reasoning, an ability central to human intelligence. Modern AI systems, including LLMs and ViTs, largely operate as sequence-of-behavior…
We design a proof system for propositional classical logic that integrates two languages for Boolean functions: standard conjunction-disjunction-negation and binary decision trees. We give two reasons to do so. The first is…
Propositional term modal logic is interpreted over Kripke structures with unboundedly many accessibility relations and hence the syntax admits variables indexing modalities and quantification over them. This logic is undecidable, and we…
One way of proving theorems in modal logics is translating them into the predicate calculus and then using conventional resolution-style theorem provers. This approach has been regarded as inappropriate in practice, because the resulting…
We classify the propositional modal validities arising from the category of sets under its natural classes of morphisms. The resulting validities depend on the morphism class, the size of the world, and the permitted substitution instances.…
Modal logic is a paradigm for several useful and applicable formal systems in computer science. It generally retains the low complexity of classical propositional logic, but notable exceptions exist in the domains of description, temporal,…
An abstract argumentation framework can be used to model the argumentative stance of an agent at a high level of abstraction, by indicating for every pair of arguments that is being considered in a debate whether the first attacks the…
In Terao [24], Hiroaki Terao defined and studied "admissible map", which is a generalization of "social welfare function" in the context of hyperplane arrangements. Using this, he proved a generalized Arrow's Impossibility Theorem using…
With help of a compact Prolog-based theorem prover for Intuitionistic Propositional Logic, we synthesize minimal assumptions under which a given formula formula becomes a theorem. After applying our synthesis algorithm to cover basic…