Related papers: Graded Distributed Belief
We propose a logic of interactive proofs as a framework for an intuitionistic foundation for interactive computation, which we construct via an interactive analog of the Goedel-McKinsey-Tarski-Artemov definition of Intuitionistic Logic as…
Knowledge graph (KG) reasoning is becoming increasingly popular in both academia and industry. Conventional KG reasoning based on symbolic logic is deterministic, with reasoning results being explainable, while modern embedding-based…
Every day, we judge the probability of propositions. When we communicate graded confidence (e.g. "I am 90% sure"), we enable others to gauge how much weight to attach to our judgment. Ideally, people should share their judgments to reach…
We explore a fuzzy modal logic that can formalise probabilistic reasoning about actions and knowledge. In particular, we deal with contexts involving statements about events expressed via modal formulas, e.g., "after doing $a$, the…
Argumentation frameworks, consisting of arguments and an attack relation representing conflicts, are fundamental for formally studying reasoning under conflicting information. We use methods from mathematical logic, specifically…
We propose modal Markov logic as an extension of propositional Markov logic to reason under the principle of maximum entropy for modal logics K45, KD45, and S5. Analogous to propositional Markov logic, the knowledge base consists of…
In previous work ("Knowledge from Probability", TARK 2021) we develop a question-relative, probabilistic account of belief. On this account, what someone believes relative to a given question is (i) closed under entailment, (ii)…
The recently initiated approach called computability logic is a formal theory of interactive computation. See a comprehensive online source on the subject at http://www.cis.upenn.edu/~giorgi/cl.html . The present paper contains a soundness…
Substantial efforts have been made in developing various Decision Modeling formalisms, both from industry and academia. A challenging problem is that of expressing decision knowledge in the context of incomplete knowledge. In such contexts,…
There exist applications of reinforcement learning like medicine where policies need to be ''interpretable'' by humans. User studies have shown that some policy classes might be more interpretable than others. However, it is costly to…
This paper presents a distributed agent-based automated theorem proving framework based on order-sorted first-order logic. Each agent in our framework has its own knowledge base, communicating to its neighboring agent(s) using…
In previous work [BGHK92, BGHK93], we have studied the random-worlds approach -- a particular (and quite powerful) method for generating degrees of belief (i.e., subjective probabilities) from a knowledge base consisting of objective…
Agents receive private signals about an unknown state. The resulting joint belief distributions are complex and lack a simple characterization. Our key insight is that, when conditioned on the state, the structure of belief distributions…
In this work, we leverage the linear algebraic structure of distributed word representations to automatically extend knowledge bases and allow a machine to learn new facts about the world. Our goal is to extract structured facts from…
We combine the concepts of modal logics and many-valued logics in a general and comprehensive way. Namely, given any finite linearly ordered set of truth values and any set of propositional connectives defined by truth tables, we define the…
Argumentation has proved a useful tool in defining formal semantics for assumption-based reasoning by viewing a proof as a process in which proponents and opponents attack each others arguments by undercuts (attack to an argument's premise)…
We motivate and describe a theory of belief in this paper. This theory is developed with the following view of human belief in mind. Consider the belief that an event E will occur (or has occurred or is occurring). An agent either…
In Non - ergodic belief networks the posterior belief OF many queries given evidence may become zero.The paper shows that WHEN belief propagation IS applied iteratively OVER arbitrary networks(the so called, iterative OR loopy belief…
We study the asymptotic learning rates under linear and log-linear combination rules of belief vectors in a distributed hypothesis testing problem. We show that under both combination strategies, agents are able to learn the truth…
A model of knowledge representation is described in which propositional facts and the relationships among them can be supported by other facts. The set of knowledge which can be supported is called the set of cognitive units, each having…