Related papers: Matching Logic
Many machine learning applications require the ability to learn from and reason about noisy multi-relational data. To address this, several effective representations have been developed that provide both a language for expressing the…
Prioritized default reasoning has illustrated its rich expressiveness and flexibility in knowledge representation and reasoning. However, many important aspects of prioritized default reasoning have yet to be thoroughly explored. In this…
We show how to give a coherent semantics to programs that are well-specified in a version of separation logic for a language with higher types: idealized algol extended with heaps (but with immutable stack variables). In particular, we…
First-order logic (FOL) has proved to be a versatile and expressive tool as the basis of abstract modeling languages. Used to verify complex systems with unbounded domains, such as heap-manipulating programs and distributed protocols, FOL,…
Relational program verification is a variant of program verification where one can reason about two programs and as a special case about two executions of a single program on different inputs. Relational program verification can be used for…
The large and still increasing popularity of deep learning clashes with a major limit of neural network architectures, that consists in their lack of capability in providing human-understandable motivations of their decisions. In situations…
Conditional logics play an important role in recent attempts to formulate theories of default reasoning. This paper investigates first-order conditional logic. We show that, as for first-order probabilistic logic, it is important not to…
Full first order linear logic can be presented as an abstract logic programming language in Miller's system Forum, which yields a sensible operational interpretation in the 'proof search as computation' paradigm. However, Forum still has to…
Dynamic logic is a powerful approach to reasoning about programs and their executions, obtained by extending classical logic with modalities that can express program executions as formulas. However, the use of dynamic logic in the setting…
Separation logic was conceived in order to make the verification of pointer programs scalable to large systems and it has proven extremely effective. The key idea is that programs typically access only small parts of memory, allowing for…
Complex logical reasoning tasks require a long sequence of reasoning, which a large language model (LLM) with chain-of-thought prompting still falls short. To alleviate this issue, neurosymbolic approaches incorporate a symbolic solver.…
Legal Judgment Prediction (LJP) is a pivotal task in legal AI. Existing semantic-enhanced LJP models integrate judicial precedents and legal knowledge for high performance. But they neglect legal reasoning logic, a critical component of…
The combination of higher-order theories and fuzzy logic can be useful in decision-making tasks that involve reasoning across abstract functions and predicates, where exact matches are often rare or unnecessary. Developing efficient…
We investigate the decidability of the definability problem for fragments of first order logic over finite words enriched with modular predicates. Our approach aims toward the most generic statements that we could achieve, which…
Over the past two decades several fragments of first-order logic have been identified and shown to have good computational and algorithmic properties, to a great extent as a result of appropriately describing the image of the standard…
Recently, symbolic structures were proposed as finite representations of potentially infinite first-order structures, where Linear Integer Arithmetic terms and formulas define the domain and interpretations of a structure. We generalize…
We present a logical separability analysis for a functional quantum computation language. This logic is inspired by previous works on logical analysis of aliasing for imperative functional programs. Both analyses share similarities notably…
In these notes we propose a new, simpler proof system for first-order matching logic with application and definedness. The new proof system is inspired by Tarski's axiomatization for first order-logic with equality (simplified by Kalish and…
In this paper we consider first-order logic theorem proving and model building via approximation and instantiation. Given a clause set we propose its approximation into a simplified clause set where satisfiability is decidable. The…
A classic result in formal language theory is the equivalence among non-counting, or aperiodic, regular languages, and languages defined through star-free regular expressions, or first-order logic. Past attempts to extend this result beyond…