Related papers: Extensions to Justification Theory
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…
One challenge in fact checking is the ability to improve the transparency of the decision. We present a fact checking method that uses reference information in knowledge graphs (KGs) to assess claims and explain its decisions. KGs contain a…
A grammar logic refers to an extension to the multi-modal logic K in which the modal axioms are generated from a formal grammar. We consider a proof theory, in nested sequent calculus, of grammar logics with converse, i.e., every modal…
We investigate some basic questions about the interaction of regular and rational relations on words. The primary motivation comes from the study of logics for querying graph topology, which have recently found numerous applications. Such…
In this paper, we advocate the use of stratified logical theories for representing probabilistic models. We argue that such encodings can be more interpretable than those obtained in existing frameworks such as Markov logic networks. Among…
The development of logic has largely been through the 'deductive' paradigm: conclusions are inferred from established premisses. However, the use of logic in the context of both human and machine reasoning is typically through the dual…
In this work, we show that both logic programming and abstract argumentation frameworks can be interpreted in terms of Nelson's constructive logic N4. We do so by formalizing, in this logic, two principles that we call non-contradictory…
An FOL-program consists of a background theory in a decidable fragment of first-order logic and a collection of rules possibly containing first-order formulas. The formalism stems from recent approaches to tight integrations of ASP with…
Approximation Fixpoint Theory (AFT) is a powerful theory covering various semantics of non-monotonic reasoning formalisms in knowledge representation such as Logic Programming and Answer Set Programming. Many semantics of such non-monotonic…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
We present an extension-based approach for computing and verifying preferences in an abstract argumentation system. Although numerous argumentation semantics have been developed previously for identifying acceptable sets of arguments from…
To appear in Theory and Practice of Logic Programming (TPLP). In this paper we propose an extension of logic programming (LP) where each default literal derived from the well-founded model is associated to a justification represented as an…
Logic has proved essential for formally modeling software based systems. Such formal descriptions, frequently called specifications, have served not only as requirements documentation and formalisation, but also for providing the…
The expression problem describes a fundamental tradeoff between two types of extensibility: extending a type with new operations, such as by pattern matching on an algebraic data type in functional programming, and extending a type with new…
Sets with atoms serve as an alternative to ZFC foundations for mathematics, where some infinite, though highly symmetric sets, behave in a finitistic way. Therefore, one can try to carry over analysis of the classical algorithms from finite…
Justification is an explanation that supports the veracity assigned to a claim in fact-checking. However, the task of justification generation is previously oversimplified as summarization of fact-check article authored by fact-checkers.…
Building on our previous work on enriched universal algebra, we define a notion of enriched language consisting of function and relation symbols whose arities are objects of the base of enrichment. In this context, we construct atomic…
We consider a simple modal logic whose non-modal part has conjunction and disjunction as connectives and whose modalities come in adjoint pairs, but are not in general closure operators. Despite absence of negation and implication, and of…
Argumentation is a central subarea of Artificial Intelligence (AI) for modeling and reasoning about arguments. The semantics of abstract argumentation frameworks (AFs) is given by sets of arguments (extensions) and conditions on the…
Argumentation is a process of evaluating and comparing a set of arguments. A way to compare them consists in using a ranking-based semantics which rank-order arguments from the most to the least acceptable ones. Recently, a number of such…