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We present Bluebell, a program logic for reasoning about probabilistic programs where unary and relational styles of reasoning come together to create new reasoning tools. Unary-style reasoning is very expressive and is powered by…
We present Behavioral Program Logic (BPL), a dynamic logic for trace properties that incorporates concepts from behavioral types and allows reasoning about non-functional properties within a sequent calculus. BPL uses behavioral modalities…
Large Language Models (LLMs) excel in complex reasoning tasks but struggle with consistent rule application, exception handling, and explainability, particularly in domains like legal analysis that require both natural language…
Definite descriptions are expressions of the form "the unique $x$ satisfying property $C$," which allow reference to objects through their distinguishing characteristics. They play a crucial role in ontology and query languages, offering an…
In this work we propose a multi-valued extension of logic programs under the stable models semantics where each true atom in a model is associated with a set of justifications, in a similar spirit than a set of proof trees. The main…
How should Large Language Model (LLM) practitioners select the right model for a task without wasting money? We introduce BELLA (Budget-Efficient LLM Selection via Automated skill-profiling), a framework that recommends optimal LLM…
We consider the call-by-value lambda-calculus extended with a may-convergent non-deterministic choice and a must-convergent parallel composition. Inspired by recent works on the relational semantics of linear logic and non-idempotent…
Recent adaptations of Large Language Models (LLMs) for time series forecasting often fail to effectively enhance information for raw series, leaving LLM reasoning capabilities underutilized. Existing prompting strategies rely on static…
Rule-based reasoning over natural language input arises in domains where decisions must be auditable and justifiable: clinical protocols specify eligibility criteria in prose, evidence rules define admissibility through textual conditions,…
We present an approach for testing student learning outcomes in a course on automated reasoning using the Isabelle proof assistant. The approach allows us to test both general understanding of formal proofs in various logical proof systems…
Elfe is an interactive system for teaching basic proof methods in discrete mathematics. The user inputs a mathematical text written in fair English which is converted to a special data-structure of first-order formulas. Certain proof…
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 apply to logic programming some recently emerging ideas from the field of reduction-based communicating systems, with the aim of giving evidence of the hidden interactions and the coordination mechanisms that rule the operational…
Technically speaking, the transcendental syntax is about designing logics with a computational foundation. It suggests a new framework for proof theory where logic (proofs, formulas, truth, ...) is no more primitive but computation is. All…
Nominal Isabelle is a definitional extension of the Isabelle/HOL theorem prover. It provides a proving infrastructure for reasoning about programming language calculi involving named bound variables (as opposed to de-Bruijn indices). In…
Reasoning about the knowledge of an attacker is a necessary step in many formal analyses of security protocols. In the framework of the applied pi calculus, as in similar languages based on equational logics, knowledge is typically…
Table Question Answering (TableQA) poses a significant challenge for large language models (LLMs) because conventional linearization of tables often disrupts the two-dimensional relationships intrinsic to structured data. Existing methods,…
The problem of mechanically formalizing and proving metatheoretic properties of programming language calculi, type systems, operational semantics, and related formal systems has received considerable attention recently. However, the dual…
LLM-generated explanations can make technical content more accessible, but there is a ceiling on what they can support interactively. Because LLM outputs are static text, they cannot be executed or stepped through. We argue that grounding…
We present a linearity theorem for a proof language of intuitionistic multiplicative additive linear logic, incorporating addition and scalar multiplication. The proofs in this language are linear in the algebraic sense. This work is part…