Related papers: Denial Logic
This article is devoted to the study of methods to change defeasible logic programs (de.l.p.s) which are the knowledge bases used by the Defeasible Logic Programming (DeLP) interpreter. DeLP is an argumentation formalism that allows to…
Studies have underscored how, regardless of the recent breakthrough and swift advances in AI research, even state-of-the-art Large Language models (LLMs) continue to struggle when performing logical and mathematical reasoning. The results…
Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a recently launched program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth that logic has more traditionally…
Standard Deontic Logic (SDL) has been used as the underlying logic to model and reason over Multi-Agent Systems governed by norms (NorMAS). It is known that SDL is not able to represent contrary-to-duty (CTD) scenarios in a consistent way.…
An inductive logic can be formulated in which the elements are not propositions or probability distributions, but information systems. The logic is complete for information systems with binary hypotheses, i.e., it applies to all such…
Differential Linear Logic enriches Linear Logic with additional logical rules for the exponential connectives, dual to the usual rules of dereliction, weakening and contraction. We present a proof-net syntax for Differential Linear Logic…
In the present work I introduce a semantics based on the cognitive attitudes of acception and rejection entertained by a given society of agents for logics inspired on Dunn and Belnap's First Degree Entailment ($\mathbf{E}$). In contrast to…
Propositional Dynamic Logic or PDL was invented as a logic for reasoning about regular programming constructs. We propose a new perspective on PDL as a multi-agent strategic logic (MASL). This logic for strategic reasoning has group…
Computational argumentation offers formal frameworks for transparent, verifiable reasoning but has traditionally been limited by its reliance on domain-specific information and extensive feature engineering. In contrast, LLMs excel at…
As large language models (LLMs) are increasing integrated into fact-checking pipelines, formal logic is often proposed as a rigorous means by which to mitigate bias, errors and hallucinations in these models' outputs. For example, some…
The use of meta-rules in logic, i.e., rules whose content includes other rules, has recently gained attention in the setting of non-monotonic reasoning: a first logical formalisation and efficient algorithms to compute the (meta)-extensions…
The framework of algorithmic knowledge assumes that agents use algorithms to compute the facts they explicitly know. In many cases of interest, a deductive system, rather than a particular algorithm, captures the formal reasoning used by…
Many applications of intelligent systems require reasoning about the mental states of agents in the domain. We may want to reason about an agent's beliefs, including beliefs about other agents; we may also want to reason about an agent's…
DLV is an efficient logic programming and non-monotonic reasoning (LPNMR) system with advanced knowledge representation mechanisms and interfaces to classic relational database systems. Its core language is disjunctive datalog…
This paper presents an extension of Defeasible Deontic Logic to deal with the Pragmatic Oddity problem. The logic applies three general principles: (1) the Pragmatic Oddity problem must be solved within a general logical treatment of CTD…
This paper presents a formal theory which describes propositional binary logic as a semantically closed formal language, and allows for syntactically and semantically well-formed formulae, formal proofs (demonstrability in Hilbertian…
We introduce negation under the stable model semantics in DatalogMTL - a temporal extension of Datalog with metric temporal operators. As a result, we obtain a rule language which combines the power of answer set programming with the…
Large Language Models (LLMs) excel at many tasks but often falter on complex problems that require structured, multi-step reasoning. We introduce the Diagram of Thought (DoT), a framework that enables a single LLM to build and navigate a…
Explanations are often promoted as tools for transparency, but they can also foster confirmation bias; users may assume reasoning is correct whenever outputs appear acceptable. We study this double-edged role of Chain-of-Thought (CoT)…
Large Language Models (LLMs) have been demonstrating strong reasoning capability with their chain-of-thoughts (CoT), which are routinely used by humans to judge answer quality. This reliance creates a powerful yet fragile basis for trust.…