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In formal epistemology, group knowledge is often modelled as the knowledge that the group would have, if the agents shared all their individual knowledge. However, this interpretation does not account for relations between agents. In this work, we propose the notion of synergistic knowledge which makes it possible to model those relationships.

Subset models provide a new semantics for justifcation logic. The main idea of subset models is that evidence terms are interpreted as sets of possible worlds. A term then justifies a formula if that formula is true in each world of the interpretation of the term. In this paper, we introduce a belief expansion operator for subset models. We study the main properties of the resulting logic as well as the differences to a previous (symbolic) approach to belief expansion in justification logic.

Different notions of the consistency of obligations collapse in standard deontic logic. In justification logics, which feature explicit reasons for obligations, the situation is different. Their strength depends on a constant specification and on the available set of operations for combining different reasons. We present different consistency principles in justification logic and compare their logical strength. We propose a novel semantics for which justification logics with the explicit version of axiom D, jd, are complete for arbitrary constant specifications. We then discuss the philosophical implications with regard to some deontic paradoxes.

Observers can glean information from others' emotional expressions through the act of drawing inferences from another individual's emotional expressions. It is important for socially aware artificial systems to be capable of doing that as it can facilitate social interaction among agents, and is particularly important in human-robot interaction for supporting a more personalized treatment of users. In this short paper, we propose a methodology for developing a formal model that allows agents to infer another agent's values from her emotion expressions.

In traditional justification logic, evidence terms have the syntactic form of polynomials, but they are not equipped with the corresponding algebraic structure. We present a novel semantic approach to justification logic that models evidence by a semiring. Hence justification terms can be interpreted as polynomial functions on that semiring. This provides an adequate semantics for evidence terms and clarifies the role of variables in justification logic. Moreover, the algebraic structure makes it possible to compute with evidence. Depending on the chosen semiring this can be used to model trust, probabilities, cost, etc. Last but not least the semiring approach seems promising for obtaining a realization procedure for modal fixed point logics.

The increasing applications of AI systems require personalized explanations for their behaviors to various stakeholders since the stakeholders may have various knowledge and backgrounds. In general, a conversation between explainers and explainees not only allows explainers to obtain the explainees' background, but also allows explainees to better understand the explanations. In this paper, we propose an approach for an explainer to communicate personalized explanations to an explainee through having consecutive conversations with the explainee. We prove that the conversation terminates due to the explainee's justification of the initial claim as long as there exists an explanation for the initial claim that the explainee understands and the explainer is aware of.

In this short note, we are concerned with the fairness condition "A and B hold almost equally often", which is important for specifying and verifying the correctness of non-terminating processes and protocols. We introduce the logic of temporal domination, in which the above condition can be expressed. We present syntax and semantics of our logic and show that it is a proper extension of linear time temporal logic. In order to obtain this result, we rely on the corresponding result for k-counting automata.

We introduce the probabilistic two-agent justification logic IPJ, a logic in which we can reason about agents that perform interactive proofs. In order to study the growth rate of the probabilities in IPJ, we present a new method of parametrising IPJ over certain negligible functions. Further, our approach leads to a new notion of zero-knowledge proofs.

Faroldi argues that deontic modals are hyperintensional and thus traditional modal logic cannot provide an appropriate formalization of deontic situations. To overcome this issue, we introduce novel justification logics as hyperintensional analogues to non-normal modal logics. We establish soundness and completeness with respect to various models and we study the problem of realization.

Controlled query evaluation (CQE) is an approach to guarantee data privacy for database and knowledge base systems. CQE-systems feature a censor function that may distort the answer to a query in order to hide sensitive information. We introduce a high-level formalization of controlled query evaluation and define several desirable properties of CQE-systems. Finally we establish two no-go theorems, which show that certain combinations of these properties cannot be obtained.

We introduce a new semantics for justification logic based on subset relations. Instead of using the established and more symbolic interpretation of justifications, we model justifications as sets of possible worlds. We introduce a new justification logic that is sound and complete with respect to our semantics. Moreover, we present another variant of our semantics that corresponds to traditional justification logic. These types of models offer us a versatile tool to work with justifications, e.g.~by extending them with a probability measure to capture uncertain justifications. Following this strategy we will show that they subsume Artemov's approach to aggregating probabilistic evidence.

The Logic of Proofs, LP, and other justification logics can have self-referential justifications of the form t:A. Such self-referential justifications are necessary for the realization of S4 in LP. Yu discovered prehistoric cycles in a particular Gentzen system as a necessary condition for S4 theorems that can only be realized using self-referentiality. It was an open problem whether prehistoric cycles also are a sufficient condition. The main results of this paper are: First, with the standard definition of self-referential theorems, prehistoric cycles are not a sufficient condition. Second, with an expansion on that definition, prehistoric cycles become sufficient for self-referential theorems.

Blockchains are distributed data structures that are used to achieve consensus in systems for cryptocurrencies (like Bitcoin) or smart contracts (like Ethereum). Although blockchains gained a lot of popularity recently, there is no logic-based model for blockchains available. We introduce BCL, a dynamic logic to reason about blockchain updates, and show that BCL is sound and complete with respect to a simple blockchain model.

Justification logics are modal-like logics with the additional capability of recording the reason, or justification, for modalities in syntactic structures, called justification terms. Justification logics can be seen as explicit counterparts to modal logics. The behavior and interaction of agents in distributed system is often modeled using logics of knowledge and time. In this paper, we sketch some preliminary ideas on how the modal knowledge part of such logics of knowledge and time could be replaced with an appropriate justification logic., Comment: In Proceedings M4M9 2017, arXiv:1703.01736

When we say "I know why he was late", we know not only the fact that he was late, but also an explanation of this fact. We propose a logical framework of "knowing why" inspired by the existing formal studies on why-questions, scientific explanation, and justification logic. We introduce the Ky_i operator into the language of epistemic logic to express "agent i knows why phi" and propose a Kripke-style semantics of such expressions in terms of knowing an explanation of phi. We obtain two sound and complete axiomatizations w.r.t. two different model classes depending on different assumptions about introspection., Comment: 34 pages, submitted, a new section added

We present the logic iJT4, which is an explicit version of intuitionistic S4 and establish soundness and completeness with respect to modular models.

We observe that justification logic enjoys a form the strong finite model property (sometimes also called small model property). Thus we obtain decidability proofs for justification logic that do not rely on Post's theorem.

We establish syntactic cut-elimination for the one-variable fragment of the modal mu-calculus. Our method is based on a recent cut-elimination technique by Mints that makes use of Buchholz' Omega-rule., Comment: In Proceedings FICS 2012, arXiv:1202.3174

Justification logics are epistemic logics that explicitly include justifications for the agents' knowledge. We develop a multi-agent justification logic with evidence terms for individual agents as well as for common knowledge. We define a Kripke-style semantics that is similar to Fitting's semantics for the Logic of Proofs LP. We show the soundness, completeness, and finite model property of our multi-agent justification logic with respect to this Kripke-style semantics. We demonstrate that our logic is a conservative extension of Yavorskaya's minimal bimodal explicit evidence logic, which is a two-agent version of LP. We discuss the relationship of our logic to the multi-agent modal logic S4 with common knowledge. Finally, we give a brief analysis of the coordinated attack problem in the newly developed language of our logic.