Related papers: Routley Star in Information-Based Semantics
We translate the argumentation networks ${\cal A}=(S, R)$ into a theory $D$ of intuitionistic logic, retaining $S$ as the domain and using intuitionistic negation to model the attack $R$ in ${\cal A}$: the attack $xRy$ is translated to…
We propose a novel framework seamlessly providing key properties of both neural nets (learning) and symbolic logic (knowledge and reasoning). Every neuron has a meaning as a component of a formula in a weighted real-valued logic, yielding a…
In the field of non-monotonic logics, the notion of Rational Closure (RC) is acknowledged as a prominent approach. In recent years, RC has gained even more popularity in the context of Description Logics (DLs), the logic underpinning the…
What is the minimal algebraic structure to reason about information flow? Do we really need the full power of Boolean algebras with co-closure and de Morgan dual operators? How much can we weaken and still be able to reason about…
Argumentation problems are concerned with determining the acceptability of a set of arguments from their relational structure. When the available information is uncertain, probabilistic argumentation frameworks provide modelling tools to…
We revisit the issue of connections between two leading formalisms in nonmonotonic reasoning: autoepistemic logic and default logic. For each logic we develop a comprehensive semantic framework based on the notion of a belief pair. The set…
The aim of the present paper is to show that the concept of intuitionistic logic based on a Heyting algebra can be generalized in such a way that it is formalized by means of a bounded poset. In this case it is not assumed that the poset is…
Large Reasoning Models (LRMs) often suffer from overthinking, generating verbose reasoning traces that compromise both computational efficiency and interpretability. Unlike prior efforts that rely on global length-based rewards, we propose…
We prove the Riemann Hypothesis via an analytically regulated surface integral over the critical strip of the Riemann zeta function. The key idea is that the convergence of this normalized integral is equivalent to the condition that all…
Modern state-of-the-art Semantic Role Labeling (SRL) methods rely on expressive sentence encoders (e.g., multi-layer LSTMs) but tend to model only local (if any) interactions between individual argument labeling decisions. This contrasts…
Retrieval-Augmented Language Models (RALMs) face significant challenges in reducing factual errors, particularly in document relevance evaluation and knowledge integration. We introduce a framework for structured relevance assessment that…
The integration of reasoning, learning, and decision-making is key to build more general artificial intelligence systems. As a step in this direction, we propose a novel neural-logic architecture, called differentiable logic machine (DLM),…
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…
Retrieval-Augmented Generation (RAG) has become a key paradigm for reducing factual hallucinations in Large Language Models (LLMs), yet little is known about how the order of retrieved documents affects model behavior. We empirically show…
Retrieval-augmented generation (RAG) relies on retrieved context to guide large language models (LLM), yet treats retrieval as a weak heuristic rather than verifiable evidence -- leading to unsupported answers, hallucinations, and reliance…
We present a system of relational syllogistic, based on classical propositional logic, having primitives of the following form: Some A are R-related to some B; Some A are R-related to all B; All A are R-related to some B; All A are…
In this paper we develop a formal system called Natural Term Logic (NTL). NTL aims to represent key aspects of the logical and grammatical mechanisms of natural language as well as grammatical transformations which preserve core logical…
Computability logic is a formal theory of computational tasks and resources. Its formulas represent interactive computational problems, logical operators stand for operations on computational problems, and validity of a formula is…
In this paper, we prove the semantic incompleteness of the Hilbert-style system for the minimal normal term-modal logic with equality and non-rigid terms that was proposed in Liberman et al. (2020) "Dynamic Term-modal Logics for First-order…
Rational decision making in its linguistic description means making logical decisions. In essence, a rational agent optimally processes all relevant information to achieve its goal. Rationality has two elements and these are the use of…