Related papers: Truth versus information in logic programming
In systems modelling, a 'system' typically comprises located resources relative to which processes execute. One important use of logic in informatics is in modelling such systems for the purpose of reasoning (perhaps automated) about their…
We extend answer set semantics to deal with inconsistent programs (containing classical negation), by finding a ``best'' answer set. Within the context of inconsistent programs, it is natural to have a partial order on rules, representing a…
Providing explanations for the outputs of artificial neural networks (ANNs) is crucial in many contexts, such as critical systems, data protection laws and handling adversarial examples. Logic-based methods can offer explanations with…
Program verification is to develop the program's proof system, and to prove the proof system soundness with respect to a trusted operational semantics of the program. However, many practical program verifiers are not based on operational…
Chain-of-thought explanations are widely used to inspect the decision process of large language models (LLMs) and to evaluate the trustworthiness of model outputs, making them important for effective collaboration between LLMs and humans.…
In this paper, we investigate proof-theoretic aspects of the logics of evidence and truth LETJ and LETF. These logics extend, respectively, Nelson's logic N and the logic of first-degree entailment FDE, also known as Belnap-Dunn four-valued…
Classically, two propositions are logically equivalent precisely when they are true under the same logical valuations. Also, two logical valuations are distinct if, and only if, there is a formula that is true according to one valuation,…
Many logic programming based approaches can be used to describe and solve combinatorial search problems. On the one hand there is constraint logic programming which computes a solution as an answer substitution to a query containing the…
It is well known that, under certain conditions, it is possible to split logic programs under stable model semantics, i.e. to divide such a program into a number of different "levels", such that the models of the entire program can be…
The paper introduces the notion of off-line justification for Answer Set Programming (ASP). Justifications provide a graph-based explanation of the truth value of an atom w.r.t. a given answer set. The paper extends also this notion to…
The generation of comprehensible explanations is an essential feature of modern artificial intelligence systems. In this work, we consider probabilistic logic programming, an extension of logic programming which can be useful to model…
We propose a stable model semantics for higher-order logic programs. Our semantics is developed using Approximation Fixpoint Theory (AFT), a powerful formalism that has successfully been used to give meaning to diverse non-monotonic…
Rules in logic programming encode information about mutual interdependencies between literals that is not captured by any of the commonly used semantics. This information becomes essential as soon as a program needs to be modified or…
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…
In this paper we present the first-order logic QLETF+, a quantified version of the logic LETF+, introduced in Coniglio and Rodrigues (Studia Logica 112:561-606, 2024). QLETF+ exhibits several properties that are not always enjoyed by logics…
Much work has been done on extending the well-founded semantics to general disjunctive logic programs and various approaches have been proposed. However, these semantics are different from each other and no consensus is reached about which…
Dynamic logic is a powerful framework for reasoning about imperative programs. An extension with a concurrent operator [18] was introduced to formalise programs running in parallel. In other direction, other authors proposed a systematic…
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…
We study transformational program logics for correctness and incorrectness that we extend to explicitly handle both termination and nontermination. We show that the logics are abstract interpretations of the right image transformer for a…
Bilattices, which provide an algebraic tool for simultaneously modelling knowledge and truth, were introduced by N.D. Belnap in a 1977 paper entitled 'How a computer should think'. Prioritised default bilattices include not only Belnap's…