Related papers: Tree-Like Justification Systems are Consistent
Justification theory is a unifying semantic framework. While it has its roots in non-monotonic logics, it can be applied to various areas in computer science, especially in explainable reasoning; its most central concept is a justification:…
Justification theory is a unifying framework for semantics of non-monotonic logics. It is built on the notion of a justification, which intuitively is a graph that explains the truth value of certain facts in a structure. Knowledge…
Justification theory is a general framework for the definition of semantics of rule-based languages that has a high explanatory potential. Nested justification systems, first introduced by Denecker et al. (2015), allow for the composition…
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…
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…
Separation Logic is a widely used formalism for describing dynamically allocated linked data structures, such as lists, trees, etc. The decidability status of various fragments of the logic constitutes a long standing open problem. Current…
An answer set is a plain set of literals which has no further structure that would explain why certain literals are part of it and why others are not. We show how argumentation theory can help to explain why a literal is or is not contained…
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…
An order-theoretic forest is a countable partial order such that the set of elements larger than any element is linearly ordered. It is an order-theoretic tree if any two elements have an upper-bound. The order type of a branch can be any…
Artificial Intelligence (AI) has long pursued models, theories, and techniques to imbue machines with human-like general intelligence. Yet even the currently predominant data-driven approaches in AI seem to be lacking humans' unique ability…
This paper will develop a single framework for unifying, simplifying and extending our prior results about axiom systems that retain a partial knowledge of their own consistency, via an axiomatic declaration of self-consistency. Its perhaps…
In the context of continuous first-order logic, special attention is often given to theories that are somehow continuous in an 'essential' way. A common feature of such theories is that they do not interpret any infinite discrete…
A fundamental question asked in modal logic is whether a given theory is consistent. But consistent with what? A typical way to address this question identifies a choice of background knowledge axioms (say, S4, D, etc.) and then shows the…
We present a new approach to the global fairness verification of tree-based classifiers. Given a tree-based classifier and a set of sensitive features potentially leading to discrimination, our analysis synthesizes sufficient conditions for…
The monadic second-order theory of trees allows quantification over elements and over arbitrary subsets. We classify the class of trees with respect to the question: does a tree T have a definable choice function (by a monadic formula with…
A central problem in proof-theory is that of finding criteria for identity of proofs, that is, for when two distinct formal derivations can be taken as denoting the same logical argument. In the literature one finds criteria which are…
Matching logic is a logical framework for specifying and reasoning about programs using pattern matching semantics. A pattern is made up of a number of structural components and constraints. Structural components are syntactically matched,…
In many situations humans have to reason with inconsistent knowledge. These inconsistencies may occur due to not fully reliable sources of information. In order to reason with inconsistent knowledge, it is not possible to view a set of…
Nonmonotonic reasoning is a pattern of reasoning that allows an agent to make and retract (tentative) conclusions from inconclusive evidence. This paper gives a possible-worlds interpretation of the nonmonotonic reasoning problem based on…
Argumentation is a non-monotonic process. This reflects the fact that argumentation involves uncertain information, and so new information can cause a change in the conclusions drawn. However, the base logic does not need to be…