Related papers: Knowledge and ignorance in Belnap--Dunn logic
Belnap-Dunn logic (BD), sometimes also known as First Degree Entailment, is a four-valued propositional logic that complements the classical truth values of True and False with two non-classical truth values Neither and Both. The latter two…
We study an extension of First Degree Entailment (FDE) by Dunn and Belnap with a non-contingency operator $\blacktriangle\phi$ which is construed as "$\phi$ has the same value in all accessible states" or "all sources give the same…
We design an expansion of Belnap--Dunn logic with belief and plausibility functions that allow non-trivial reasoning with inconsistent and incomplete probabilistic information. We also formalise reasoning with non-standard probabilities and…
We explore the problem of explaining observations starting from a classically inconsistent theory by adopting a paraconsistent framework. We consider two expansions of the well-known Belnap--Dunn paraconsistent four-valued logic…
Belief and plausibility are weaker measures of uncertainty than that of probability. They are motivated by the situations when full probabilistic information is not available. However, information can also be contradictory. Therefore, the…
Belnap-Dunn's relevance logic, BD, was designed seeking a suitable logical device for dealing with multiple information sources which sometimes may provide inconsistent and/or incomplete pieces of information. BD is a four-valued logic…
Recently, interpretable machine learning has re-explored concept bottleneck models (CBM). An advantage of this model class is the user's ability to intervene on predicted concept values, affecting the downstream output. In this work, we…
The recent series of innovations in deep learning (DL) have shown enormous potential to impact individuals and society, both positively and negatively. The DL models utilizing massive computing power and enormous datasets have significantly…
Bilattices provide an algebraic tool with which to model simultaneously knowledge and truth. They were introduced by Belnap in 1977 in a paper entitled \emph{How a computer should think}. Belnap argued that instead of using a logic with two…
Recent years witnessed a growing interest in non-standard epistemic logics of knowing whether, knowing how, knowing what, knowing why and so on. The new epistemic modalities introduced in those logics all share, in their semantics, the…
Deep Neural Networks (DNNs) do not inherently compute or exhibit empirically-justified task confidence. In mission critical applications, it is important to both understand associated DNN reasoning and its supporting evidence. In this…
Knowledge base completion (KBC) aims to automatically infer missing facts by exploiting information already present in a knowledge base (KB). A promising approach for KBC is to embed knowledge into latent spaces and make predictions from…
Recent advances in deep learning have led to increasingly complex models with deeper layers and more parameters, reducing interpretability and making their decisions harder to understand. While many methods explain black-box reasoning, most…
In this work, we consider the long-standing open question of constructing constant-round concurrent zero-knowledge protocols in the plain model. Resolving this question is known to require non-black-box techniques. We consider non-black-box…
Modern deep neural networks have now reached human-level performance across a variety of tasks. However, unlike humans they lack the ability to explain their decisions by showing where and telling what concepts guided them. In this work, we…
In recent work, Stalnaker proposes a logical framework in which belief is realized as a weakened form of knowledge. Building on Stalnaker's core insights, and using frameworks developed by Bjorndahl and Baltag et al., we employ topological…
Blast furnace modeling and control is one of the important problems in the industrial field, and the black-box model is an effective mean to describe the complex blast furnace system. In practice, there are often different learning targets,…
We investigate the problem of reasoning in the propositional fragment of MBNF, the logic of minimal belief and negation as failure introduced by Lifschitz, which can be considered as a unifying framework for several nonmonotonic formalisms,…
In recent work, Stalnaker proposes a logical framework in which belief is realized as a weakened form of knowledge. Building on Stalnaker's core insights, and using frameworks developed in previous work by Bjorndahl and Baltag et al., we…
A recent line of research has developed around logics of belief based on evidence. The approach of B\'ilkov\'a et al understands belief as based on information confirmed by a reliable source. We propose a finer analysis of how belief can be…