Related papers: Common knowledge logic in a higher order proof ass…
Modifiable combining functions are a synthesis of two common approaches to combining evidence. They offer many of the advantages of these approaches and avoid some disadvantages. Because they facilitate the acquisition, representation,…
Automated theorem proving has long been a key task of artificial intelligence. Proofs form the bedrock of rigorous scientific inquiry. Many tools for both partially and fully automating their derivations have been developed over the last…
The intuitive notion of evidence has both semantic and syntactic features. In this paper, we develop an {\em evidence logic} for epistemic agents faced with possibly contradictory evidence from different sources. The logic is based on a…
The need for formal definition of the very basis of mathematics arose in the last century. The scale and complexity of mathematics, along with discovered paradoxes, revealed the danger of accumulating errors across theories. Although,…
Most existing work on strategic reasoning simply adopts either an informed or an uninformed semantics. We propose a model where knowledge of strategies can be specified on a fine-grained level. In particular, it is possible to distinguish…
To appear in Theory and Practice of Logic Programming (TPLP), Proceedings of ICLP 2015 Recent advances in knowledge compilation introduced techniques to compile \emph{positive} logic programs into propositional logic, essentially exploiting…
Conceptualization, or viewing entities and situations as instances of abstract concepts in mind and making inferences based on that, is a vital component in human intelligence for commonsense reasoning. Despite recent progress in artificial…
This paper describes a formal proof library, developed using the Coq proof assistant, designed to assist users in writing correct diagrammatic proofs, for 1-categories. This library proposes a deep-embedded, domain-specific formal language,…
First-order logic is the basis for many knowledge representation formalisms and methods. Providing technological support for learning to write first-order formulas for natural language specifications requires methods to test formulas for…
When we communicate with other humans, we do not simply generate a sequence of words. Rather, we use our cognitive state (beliefs, desires, intentions) and our model of the audience's cognitive state to create utterances that affect the…
We present a logical system that combines the well-known classical epistemic concepts of belief and knowledge with a concept of evidence such that the intuitive principle \textit{`evidence yields belief and knowledge'} is satisfied. Our…
In domains with high knowledge distribution a natural objective is to create principle foundations for collaborative interactive learning environments. We present a first mathematical characterization of a collaborative learning group, a…
Highly automated theorem provers like Dafny allow users to prove simple properties with little effort, making it easy to quickly sketch proofs. The drawback is that such provers leave users with little control about the proof search,…
The ability of an agent to comprehend a sentence is tightly connected to the agent's prior experiences and background knowledge. The paper suggests to interpret comprehension as a modality and proposes a complete bimodal logical system that…
Proof assistants are software-based tools that are used in the mechanization of proof construction and validation in mathematics and computer science, and also in certified program development. Different tools are being increasingly used in…
Commonsense knowledge-graphs (CKGs) are important resources towards building machines that can 'reason' on text or environmental inputs and make inferences beyond perception. While current CKGs encode world knowledge for a large number of…
We present a tool for modelling and reasoning with knowledge from various diverse (and possibly conflicting) viewpoints. The theoretical underpinnings are provided by enhancing base logics by standpoints according to a recently introduced…
We formulate and prove an Agreement Theorem for quantum mechanics (QM), describing when two agents, represented by separate laboratories, can or cannot maintain differing probability estimates of a shared quantum property of interest.…
A fundamental ability of humans is to utilize commonsense knowledge in language understanding and question answering. In recent years, many knowledge-enhanced Commonsense Question Answering (CQA) approaches have been proposed. However, it…
Homotopy type theory is an interpretation of Martin-L\"of's constructive type theory into abstract homotopy theory. There results a link between constructive mathematics and algebraic topology, providing topological semantics for…