Related papers: Parameterized Dynamic Logic -- Towards A Cyclic Lo…
Relying on the formulae-as-types paradigm for classical logic, we define a program logic for an imperative language with higher-order procedural variables and non-local jumps. Then, we show how to derive a sound program logic for this…
Real world systems of interest often feature interactions between discrete and continuous dynamics. Various hybrid system formalisms have been used to model and analyze this combination of dynamics, ranging from mathematical descriptions,…
The ability of Large Language Models (LLMs) to perform reasoning tasks such as deduction has been widely investigated in recent years. Yet, their capacity to generate proofs-faithful, human-readable explanations of why conclusions…
Relational properties arise in many settings: relating two versions of a program that use different data representations, noninterference properties for security, etc. The main ingredient of relational verification, relating aligned pairs…
LPTP (Logic Program Theorem Prover) is an interactive natural-deduction-based theorem prover for pure Prolog programs with negation as failure, unification with the occurs check, and a restricted but extensible set of built-in predicates.…
In this paper we propose a many-valued temporal conditional logic. We start from a many-valued logic with typicality, and extend it with the temporal operators of the Linear Time Temporal Logic (LTL), thus providing a formalism which is…
Effectively translating between natural language (NL) and formal logics like Linear Temporal Logic (LTL) requires expertise that limits formal verification's reach in safety-critical development. Template-based approaches sacrifice…
We propose a novel approach for the formal verification of biological systems based on the use of a modal linear logic. We show how such a logic can be used, with worlds as instants of time, as an unified framework to encode both biological…
Formal verification provides strong guarantees of correctness of software, which are especially important in safety or security critical systems. Hoare logic is a widely used formalism for rigorous verification of software against…
We propose a novel architecture for integrating large language models (LLMs) with a persistent, interactive Lisp environment. This setup enables LLMs to define, invoke, and evolve their own tools through programmatic interaction with a live…
In this position paper, we propose a reasoning framework that can model the reasoning process underlying natural language inferences. The framework is based on the semantic tableau method, a well-studied proof system in formal logic. Like…
In this paper we propose an approach to reasoning about properties of imperative programs. We assume in this context that the meanings of program constructs are described using rules in the natural semantics style with the additional…
Large Language Models (LLMs) have emerged as a promising alternative to traditional static program analysis methods, such as symbolic execution, offering the ability to reason over code directly without relying on theorem provers or SMT…
We introduce SMProbLog, a generalization of the probabilistic logic programming language ProbLog. A ProbLog program defines a distribution over logic programs by specifying for each clause the probability that it belongs to a randomly…
Probabilistic Logic Programming (PLP) under the Distribution Semantics is a leading approach to practical reasoning under uncertainty. An advantage of the Distribution Semantics is its suitability for implementation as a Prolog or Python…
While Large Language Models (LLMs) can solve many NLP tasks in zero-shot settings, applications involving embodied agents remain problematic. In particular, complex plans that require multi-step reasoning become difficult and too costly as…
The programming language Prolog makes declarative programming possible, at least to a substantial extent. Programs may be written and reasoned about in terms of their declarative semantics. All the advantages of declarative programming are…
Description logic programs (dl-programs) under the answer set semantics formulated by Eiter {\em et al.} have been considered as a prominent formalism for integrating rules and ontology knowledge bases. A question of interest has been…
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 study a many-valued generalization of Propositional Dynamic Logic where formulas in states and accessibility relations between states of a Kripke model are evaluated in a finite FL-algebra. One natural interpretation of this framework is…