Related papers: A two-level logic approach to reasoning about comp…
Natural language reasoning plays an increasingly important role in improving language models' ability to solve complex language understanding tasks. An interesting use case for reasoning is the resolution of context-dependent ambiguity. But…
We advocate a declarative approach to proving properties of logic programs. Total correctness can be separated into correctness, completeness and clean termination; the latter includes non-floundering. Only clean termination depends on the…
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…
We study the expressive power of the two-variable fragment of order-invariant first-order logic. This logic departs from first-order logic in two ways: first, formulas are only allowed to quantify over two variables. Second, formulas can…
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…
GL is a verified tool for proving ACL2 theorems using Boolean methods such as BDD reasoning and satisfiability checking. In its typical operation, GL recursively traverses a term, computing a symbolic object representing the value of each…
The complexity of modern software systems entails the need for reconfiguration mechanisms gov- erning the dynamic evolution of their execution configurations in response to both external stimulus or internal performance measures. Formally,…
We show a projective Beth definability theorem for logic programs under the stable model semantics: For given programs $P$ and $Q$ and vocabulary $V$ (set of predicates) the existence of a program $R$ in $V$ such that $P \cup R$ and $P \cup…
Traditional symbolic reasoning engines, while attractive for their precision and explicability, have a few major drawbacks: the use of brittle inference procedures that rely on exact matching (unification) of logical terms, an inability to…
We report on the mechanization of (preference-based) conditional normative reasoning. Our focus is on Aqvist's system E for conditional obligation, and its extensions. Our mechanization is achieved via a shallow semantical embedding in…
We present the guarded lambda-calculus, an extension of the simply typed lambda-calculus with guarded recursive and coinductive types. The use of guarded recursive types ensures the productivity of well-typed programs. Guarded recursive…
Extensive research on formal verification of machine learning systems indicates that learning from data alone often fails to capture underlying background knowledge, such as specifications implicitly available in the data. Various neural…
We propose a new formalism for specifying and reasoning about problems that involve heterogeneous "pieces of information" -- large collections of data, decision procedures of any kind and complexity and connections between them. The essence…
First-Order Logic (FOL) is widely regarded as one of the most important foundations for knowledge representation. Nevertheless, in this paper, we argue that FOL has several critical issues for this purpose. Instead, we propose an…
We define a logic of propositional formula schemata adding to the syntax of propositional logic indexed propositions and iterated connectives ranging over intervals parameterized by arithmetic variables. The satisfiability problem is shown…
OWL 2 has been standardized by the World Wide Web Consortium (W3C) as a family of ontology languages for the Semantic Web. The most expressive of these languages is OWL 2 Full, but to date no reasoner has been implemented for this language.…
A logic is defined that allows to express information about statistical probabilities and about degrees of belief in specific propositions. By interpreting the two types of probabilities in one common probability space, the semantics given…
Inconsistency handling is an important issue in knowledge management. Especially in ontology engineering, logical inconsistencies may occur during ontology construction. A natural way to reason with an inconsistent ontology is to utilize…
The theory of finite term algebras provides a natural framework to describe the semantics of functional languages. The ability to efficiently reason about term algebras is essential to automate program analysis and verification for…
We analyse so-called computable laws, i.e., laws that can be enforced by automatic procedures. These laws should be logically perfect and unambiguous, but sometimes they are not. We use a regulation on road transport to illustrate this…