Related papers: Logical Relations for Partial Features and Automat…
Principles of analogical reasoning have recently been applied in the context of machine learning, for example to develop new methods for classification and preference learning. In this paper, we argue that, while analogical reasoning is…
The advancement of Large Language Models (LLMs) has greatly improved our ability to process complex language. However, accurately detecting logical fallacies remains a significant challenge. This study presents a novel and effective prompt…
We extend description logics (DLs) with non-monotonic reasoning features. We start by investigating a notion of defeasible subsumption in the spirit of defeasible conditionals as studied by Kraus, Lehmann and Magidor in the propositional…
Pitts and Stark's $\nu$-calculus is a paradigmatic total language for studying the problem of contextual equivalence in higher-order languages with name generation. Models for the $\nu$-calculus that validate basic equivalences concerning…
This paper introduces Logical Credal Networks, an expressive probabilistic logic that generalizes many prior models that combine logic and probability. Given imprecise information represented by probability bounds and conditional…
Remarkable progress has been made on automated reasoning with natural text, by using Language Models (LMs) and methods such as Chain-of-Thought and Selection-Inference. These techniques search for proofs in the forward direction from axioms…
In relational verification, judicious alignment of computational steps facilitates proof of relations between programs using simple relational assertions. Relational Hoare logics (RHL) provide compositional rules that embody various…
This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…
The purpose of this paper is to introduce justification logics based on conditional logics. We introduce a new family of logics, called conditional justification logics, which incorporates a counterfactual conditional in its language. For…
Differential logical relations are methods to measure distances between higher-order programs where distances between functional programs are themselves \emph{functions}, relating errors in inputs with errors in outputs. This way,…
We propose abstract compilation for precise static type analysis of object-oriented languages based on coinductive logic programming. Source code is translated to a logic program, then type-checking and inference problems amount to queries…
Biases in large language models (LLMs) often manifest as systematic distortions in associations between demographic attributes and professional or social roles, reinforcing harmful stereotypes across gender, ethnicity, and geography. This…
Arguments are a fundamental aspect of human reasoning, in which claims are supported, challenged, and weighed against one another. We present an end-to-end large language model (LLM)-based system for reconstructing arguments from natural…
Type-and-effect systems incorporate information about the computational effects, e.g., state mutation, probabilistic choice, or I/O, a program phrase may invoke alongside its return value. A semantics for type-and-effect systems involves a…
Recently, Multimodal Large Language Models (MLLMs) have achieved significant success across multiple disciplines due to their exceptional instruction-following capabilities and extensive world knowledge. However, whether these MLLMs possess…
This paper explores relational syllogistic logics, a family of logical systems related to reasoning about relations in extensions of the classical syllogistic. These are all decidable logical systems. We prove completeness theorems and…
Category theory can be used to state formulas in First-Order Logic without using set membership. Several notable results in logic such as proof of the continuum hypothesis can be elegantly rewritten in category theory. We propose in this…
Types in logic programming have focused on conservative approximations of program semantics by regular types, on one hand, and on type systems based on a prescriptive semantics defined for typed programs, on the other. In this paper, we…
Large Language Models (LLMs) have made significant strides in various intelligent tasks but still struggle with complex action reasoning tasks that require systematic search. To address this limitation, we propose a method that bridges the…
We generalize Kracht's theory of internal describability from classical modal logic to the family of all logics canonically associated with varieties of normal lattice expansions (LE algebras). We work in the purely algebraic setting of…