Related papers: On Strong and Default Negation in Logic Program Up…
In this paper, we revisit the task of negation resolution, which includes the subtasks of cue detection (e.g. "not", "never") and scope resolution. In the context of previous shared tasks, a variety of evaluation metrics have been proposed.…
Answer substitutions play a central role in logic programming. To support {\it selective} answer substitutions, we refine $\exists x$ in goals into two different versions: the noisy version $\exists^o x$ and the silent version $\exists x$.…
Nested logic programs have recently been introduced in order to allow for arbitrarily nested formulas in the heads and the bodies of logic program rules under the answer sets semantics. Nested expressions can be formed using conjunction,…
Despite rapid adoption of autoregressive large language models, smaller text encoders still play an important role in text understanding tasks that require rich contextualized representations. Negation is an important semantic function that…
In this paper, we present two alternative approaches to defining answer sets for logic programs with arbitrary types of abstract constraint atoms (c-atoms). These approaches generalize the fixpoint-based and the level mapping based answer…
Logics for knowledge representation suffer from over-specialization: while each logic may provide an ideal representation formalism for some problems, it is less than optimal for others. A solution to this problem is to choose from several…
Large language models (LLMs) take advantage of step-by-step reasoning instructions, e.g., chain-of-thought (CoT) prompting. Building on this, their ability to perform CoT-style reasoning robustly is of interest from a probing perspective.…
Termination of logic programs with negated body atoms (here called general logic programs) is an important topic. One reason is that many computational mechanisms used to process negated atoms, like Clark's negation as failure and Chan's…
Non-classical negations may fail to be contradictory-forming operators in more than one way, and they often fail also to respect fundamental meta-logical properties such as the replacement property. Such drawbacks are witnessed by intricate…
Given a set of Datalog rules, facts, and a query, answers to the query can be inferred bottom-up starting from the facts or top-down starting from the query. For efficiency, top-down evaluation is extended with memoization of inferred…
Understanding and solving complex reasoning tasks is vital for addressing the information needs of a user. Although dense neural models learn contextualised embeddings, they still underperform on queries containing negation. To understand…
Argumentation has proved a useful tool in defining formal semantics for assumption-based reasoning by viewing a proof as a process in which proponents and opponents attack each others arguments by undercuts (attack to an argument's premise)…
In answer set programming, two groups of rules are considered strongly equivalent if they have the same meaning in any context. Strong equivalence of two programs can be sometimes established by deriving rules of each program from rules of…
Logic programming, as exemplified by datalog, defines the meaning of a program as its unique smallest model: the deductive closure of its inference rules. However, many problems call for an enumeration of models that vary along some set of…
Argumentation is a very active research field of Artificial Intelligence concerned with the representation and evaluation of arguments used in dialogues between humans and/or artificial agents. Acceptability semantics of formal…
As machine translation (MT) systems progress at a rapid pace, questions of their adequacy linger. In this study we focus on negation, a universal, core property of human language that significantly affects the semantics of an utterance. We…
Negation is an important perspective of knowledge representation. Existing negation methods are mainly applied in probability theory, evidence theory and complex evidence theory. As a generalization of evidence theory, random permutation…
Partial correctness of imperative or functional programming divides in logic programming into two notions. Correctness means that all answers of the program are compatible with the specification. Completeness means that the program produces…
This paper describes a simpler way for programmers to reason about the correctness of their code. The study of semantics of logic programs has shown strong links between the model theoretic semantics (truth and falsity of atoms in the…
We extend the epistemic logic with De Morgan negation by Fagin et al. (Artif. Intell. 79, 203-240, 1995) by adding operators for universal and common knowledge in a group of agents, and with a formalization of information update using a…