Related papers: Deductive Systems for Logic Programs with Counting
We show that strict deterministic propositional dynamic logic with intersection is highly undecidable, solving a problem in the Stanford Encyclopedia of Philosophy. In fact we show something quite a bit stronger. We introduce the…
Open logic programs and open entailment have been recently proposed as an abstract framework for the verification of incomplete specifications based upon normal logic programs and the stable model semantics. There are obvious analogies…
By incorporating the methods of Answer Set Programming (ASP) and Markov Logic Networks (MLN), LPMLN becomes a powerful tool for non-monotonic, inconsistent and uncertain knowledge representation and reasoning. To facilitate the applications…
Answer Set Programming (ASP) is a successful method for solving a range of real-world applications. Despite the availability of fast ASP solvers, computing answer sets demands a very large computational power, since the problem tackled is…
We propose an operationally-based deductive proof method for program equivalence. It is based on encoding the language semantics as logically constrained term rewriting systems (LCTRSs) and the two programs as terms. The main feature of our…
We define an algorithm to be the set of programs that implement or express that algorithm. The set of all programs is partitioned into equivalence classes. Two programs are equivalent if they are essentially the same program. The set of…
Epistemic Logic Programs (ELPs) extend Answer Set Programming (ASP) with epistemic negation and have received renewed interest in recent years. This led to the development of new research and efficient solving systems for ELPs. In practice,…
Functional languages with strong static type systems have beneficial properties to help ensure program correctness and reliability. Surprisingly, their practical significance in applications is low relative to other languages lacking in…
Existing math datasets evaluate the reasoning abilities of large language models (LLMs) by either using the final answer or the intermediate reasoning steps derived from static examples. However, the former approach fails to surface model's…
We study bisimulation and context equivalence in a probabilistic $\lambda$-calculus. The contributions of this paper are threefold. Firstly we show a technique for proving congruence of probabilistic applicative bisimilarity. While the…
We define a bi-directional embedding between hypersequent calculi and a subclass of systems of rules (2-systems). In addition to showing that the two proof frameworks have the same expressive power, the embedding allows for the recovery of…
Abductive logic programs offer a formalism to declaratively represent and reason about problems in a variety of areas: diagnosis, decision making, hypothetical reasoning, etc. On the other hand, logic program updates allow us to express…
Existing refinement calculi provide frameworks for the stepwise development of imperative programs from specifications. This paper presents a refinement calculus for deriving logic programs. The calculus contains a wide-spectrum logic…
In this work we present work in progress on functionality duplication detection in logic programs. Eliminating duplicated functionality recently became prominent in context of refactoring. We describe a quantitative approach that allows to…
The framework of algorithmic knowledge assumes that agents use algorithms to compute the facts they explicitly know. In many cases of interest, a deductive system, rather than a particular algorithm, captures the formal reasoning used by…
Testing algorithms across a wide range of problem instances is crucial to ensure the validity of any claim about one algorithm's superiority over another. However, when it comes to inference algorithms for probabilistic logic programs,…
Modular logic programs provide a way of viewing logic programs as consisting of many independent, meaningful modules. This paper introduces first-order modular logic programs, which can capture the meaning of many answer set programs. We…
We target the problem of automatically synthesizing proofs of semantic equivalence between two programs made of sequences of statements. We represent programs using abstract syntax trees (AST), where a given set of semantics-preserving…
We present a system for generating parsers based directly on the metaphor of parsing as deduction. Parsing algorithms can be represented directly as deduction systems, and a single deduction engine can interpret such deduction systems so as…
Separation Logic with inductive definitions is a well-known approach for deductive verification of programs that manipulate dynamic data structures. Deciding verification conditions in this context is usually based on user-provided lemmas…