Related papers: Common knowledge logic in a higher order proof ass…
The paper proposes a bimodal logic that describes an interplay between distributed knowledge modality and coalition know-how modality. Unlike other similar systems, the one proposed here assumes perfect recall by all agents. Perfect recall…
An introduction is given to an algebraic formulation and generalisation of the consistent histories approach to quantum theory. The main technical tool in this theory is an orthoalgebra of history propositions that serves as a generalised…
Isabelle is an interactive theorem prover that supports a variety of logics. It represents rules as propositions (not as functions) and builds proofs by combining rules. These operations constitute a meta-logic (or `logical framework') in…
Uniform proofs are sequent calculus proofs with the following characteristic: the last step in the derivation of a complex formula at any stage in the proof is always the introduction of the top-level logical symbol of that formula. We…
In this paper, we present an alternative interpretation of propositional inquisitive logic as an epistemic logic of knowing how. In our setting, an inquisitive logic formula $\alpha$ being supported by a state is formalized as "knowing how…
We report on the development of the HoTT library, a formalization of homotopy type theory in the Coq proof assistant. It formalizes most of basic homotopy type theory, including univalence, higher inductive types, and significant amounts of…
Uniform interpolation is the property that, for any formula and set of atoms, there exists the strongest consequence omitting those atoms. It plays a central role in knowledge representation and reasoning tasks such as knowledge update and…
The importance of category theory in recent developments in both mathematics and in computer science cannot be overstated. However, its abstract nature makes it difficult to understand at first. Graphical languages have been developed to…
We define the concept of collaborative theorem proving and outline our plan to make it a reality. We believe that a successful implementation of collaborative theorem proving is a necessary prerequisite for the formal verification of large…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
Cooperation information sharing is important to theories of human learning and has potential implications for machine learning. Prior work derived conditions for achieving optimal Cooperative Inference given strong, relatively restrictive…
We present a model of sense-making that greatly facilitates the collaboration between an intelligent analyst and a knowledge-based agent. It is a general model grounded in the science of evidence and the scientific method of hypothesis…
The ability to automatically generalise (interactive) proofs and use such generalisations to discharge related conjectures is a very hard problem which remains unsolved. Here, we develop a notion of goal types to capture key properties of…
We present an architecture for ad hoc teamwork, which refers to collaboration in a team of agents without prior coordination. State of the art methods for this problem often include a data-driven component that uses a long history of prior…
Due to their numerous advantages, formal proofs and proof assistants, such as Coq, are becoming increasingly popular. However, one disadvantage of using proof assistants is that the resulting proofs can sometimes be hard to read and…
Knowledge facts are typically represented by relational triples, while we observe that some commonsense facts are represented by the triples whose forms are inconsistent with the expression of language. This inconsistency puts forward a…
In a 1985 commentary to his collected works, Kolmogorov informed the reader that his 1932 paper 'On the interpretation of intuitionistic logic' "was written in hope that with time, the logic of solution of problems [i.e., intuitionistic…
In recent years, epistemic logics have been extended with operators K_ax for knowledge of (the value of) a variable x (by an agent a). We study dynamic versions of these logics, enriched with modalities for semi-public data-exchange events…
We investigate the complexity of the satisfiability problem for a modal logic expressing `knowing how' assertions, related to an agent's abilities to achieve a certain goal. We take one of the most standard semantics for this kind of logics…
According to Aumann's celebrated theorem, rational agents cannot agree to disagree. In other words, agents who once shared a common prior probability distribution and who have common knowledge about their posteriors cannot assign different…