Related papers: Rewriting Induction for Existentially Quantified E…

Quotient inductive-inductive types (QIITs) are generalized inductive types which allow sorts to be indexed over previously declared sorts, and allow usage of equality constructors. QIITs are especially useful for algebraic descriptions of…

This paper addresses the problem of creating simplifiers for logic formulas based on conditional term rewriting. In particular, the paper focuses on a program synthesis application where formula simplifications have been shown to have a…

With this work, we describe the concept of intent-based query rewriting and present a first viable solution. The aim is to allow rewrites to alter the structure and syntactic outcome of an original query while keeping the obtainable…

Recent works have shown that attaching prompts to the input is effective at conditioning Language Models (LM) to perform specific tasks. However, prompts are always included in the input text during inference, thus incurring substantial…

Induction is typically formalized as a rule or axiom extension of the LK-calculus. While this extension of the sequent calculus is simple and elegant, proof transformation and analysis can be quite difficult. Theories with an induction…

Propositional inquisitive logic is the limit of its $n$-bounded approximations. In the predicate setting, however, this does not hold anymore, as discovered by Ciardelli and Grilletti, who also found complete axiomatizations of $n$-bounded…

Integrating causal inference (CI) with reinforcement learning (RL) has emerged as a powerful paradigm to address critical limitations in classical RL, including low explainability, lack of robustness and generalization failures. Traditional…

After surveying classical results, we introduce a generalized notion of inference system to support structural recursion on non-well-founded data types. Besides axioms and inference rules with the usual meaning, a generalized inference…

Rewriting logic is naturally concurrent: several subterms of the state term can be rewritten simultaneously. But state terms are global, which makes compositionality difficult to achieve. Compositionality here means being able to decompose…

In this contribution we revisit regular model checking, a powerful framework that has been successfully applied for the verification of infinite-state systems, especially parameterized systems (concurrent systems with an arbitrary number of…

Reinforcement Learning with Verifiable Rewards (RLVR) has proven effective for complex reasoning tasks with clear correctness signals such as math and coding. However, extending it to real-world reasoning tasks is challenging, as evaluation…

On the topic of probabilistic rewriting, there are several works studying both termination and confluence of different systems. While working with a lambda calculus modelling quantum computation, we found a system with probabilistic…

Constructor-Based Conditional Rewriting Logic is a general framework for integrating first-order functional and logic programming which gives an algebraic semantics for non-deterministic functional-logic programs. In the context of this…

We revisit evaluation of logical formulas that allow both uninterpreted relations, constrained to be finite, as well as an interpreted vocabulary over an infinite domain. This formalism was denoted embedded finite model theory in the past.…

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 highlight how Rule-based Integration (Rubi) is an enhanced method of symbolic integration which allows for the integration of many difficult integrals not accomplished by other computer algebra systems. Using Rubi, many integration…

While model checking has often been considered as a practical alternative to building formal proofs, we argue here that the theory of sequent calculus proofs can be used to provide an appealing foundation for model checking. Since the…

Legal rules encompass not only codified statutes but also implicit adjudicatory principles derived from precedents that contain discretionary norms, social morality, and policy. While computational legal research has advanced in applying…

Numerous confluence criteria for plain term rewrite systems are known. For logically constrained rewrite system, an attractive extension of term rewriting in which rules are equipped with logical constraints, much less is known. In this…

The lambda Pi calculus can be extended with rewrite rules to embed any functional pure type system. In this paper, we show that the embedding is conservative by proving a relative form of normalization, thus justifying the use of the lambda…