相关论文: Many Logics, One Methodology: A Plea for Logical P…

This paper presents meta-logical investigations based on category theory using the proof assistant Isabelle/HOL. We demonstrate the potential of a free logic based shallow semantic embedding of category theory by providing a formalization…

Program logics for bug-finding (such as the recently introduced Incorrectness Logic) have framed correctness and incorrectness as dual concepts requiring different logical foundations. In this paper, we argue that a single unified theory…

In this work, we introduce Contextual Analog Logic with Multimodality (CALM). CALM unites symbolic reasoning with neural generation, enabling systems to make context-sensitive decisions grounded in real-world multi-modal data. Background:…

We explore a kind of first-order predicate logic with intended semantics in the reals. Compared to other approaches in the literature, we work predominantly in the multiplicative reals $[0,\infty]$, showing they support three generations of…

The goal of this paper is to extend classical logic with a generalized notion of inductive definition supporting positive and negative induction, to investigate the properties of this logic, its relationships to other logics in the area of…

Libraries of formal proofs are an important part of our mathematical heritage, but their usability and sustainability is poor. Indeed, each library is specific to a proof system, sometimes even to some version of this system. Thus, a…

The Logic of Proofs, LP, and its successor, Justification Logic, is a refinement of the modal logic approach to epistemology in which proofs/justifications are taken into account. In 2000 Kuznets showed that satisfiability for LP is in the…

Logic programming is a flexible programming paradigm due to the use of predicates without a fixed data flow. To extend logic languages with the compact notation of functional programming, there are various proposals to map evaluable…

To appear in Theory and Practice of Logic Programming (TPLP). Tabling is a commonly used technique in logic programming for avoiding cyclic behavior of logic programs and enabling more declarative program definitions. Furthermore, tabling…

We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…

With the increasing capabilities of Large Language Models (LLMs), parallel reasoning has emerged as a new inference paradigm that enhances reasoning robustness by concurrently exploring multiple lines of thought before converging on a final…

Rule-based reasoning is an essential part of human intelligence prominently formalized in artificial intelligence research via logic programs. Describing complex objects as the composition of elementary ones is a common strategy in computer…

Isabelle is an interactive theorem prover that supports a variety of logics. It represents rules as propositions (not as functions) and builds proofs by combining rules. These operations constitute a meta-logic (or `logical framework') in…

Informal logic is a method of argument analysis which is complementary to that of formal logic, providing for the pragmatic treatment of features of argumentation which cannot be reduced to logical form. The central claim of this paper is…

Interactive Information Retrieval refers to the branch of Information Retrieval that considers the retrieval process with respect to a wide range of contexts, which may affect the user's information seeking experience. The identification…

In this paper we show several similarities among logic systems that deal simultaneously with deductive and quantitative inference. We claim it is appropriate to call the tasks those systems perform as Quantitative Logic Reasoning. Analogous…

This work discusses how to build more rational language and multimodal agents and what criteria define rationality in intelligent systems. Rationality is the quality of being guided by reason, characterized by decision-making that aligns…

Given a set of conflicting arguments, there can exist multiple plausible opinions about which arguments should be accepted, rejected, or deemed undecided. We study the problem of how multiple such judgments can be aggregated. We define the…

Similarity in formal argumentation has recently gained attention due to its significance in problems such as argument aggregation in semantics and enthymeme decoding. While existing approaches focus on propositional logic, we address the…

In this paper we present a formalization of Intuitionistic Propositional Logic in the Lean proof assistant. Our approach focuses on verifying two completeness proofs for the studied logical system, as well as exploring the relation between…