Related papers: Layered Fixed Point Logic
Linear logic provides a framework to control the complexity of higher-order functional programs. We present an extension of this framework to programs with multithreading and side effects focusing on the case of elementary time. Our main…
We analyze the problem of defining well-founded semantics for ordered logic programs within a general framework based on alternating fixpoint theory. We start by showing that generalizations of existing answer set approaches to preference…
Tractability results for the model checking problem of logics yield powerful algorithmic meta theorems of the form: Every computational problem expressible in a logic $L$ can be solved efficiently on every class $\mathscr{C}$ of structures…
A new method of deriving comparative statics information using generalized compensated derivatives is presented which yields constraint-free semidefiniteness results for any differentiable, constrained optimization problem. More generally,…
Fuzzy logic programming is an established approach for reasoning under uncertainty. Several semantics from classical, two-valued logic programming have been generalized to the case of fuzzy logic programs. In this paper, we show that two of…
We introduce a lazy approach to the explanation-based approximation of probabilistic logic programs. It uses only the most significant part of the program when searching for explanations. The result is a fast and anytime approximate…
Logic-based approaches to AI have the advantage that their behavior can in principle be explained to a user. If, for instance, a Description Logic reasoner derives a consequence that triggers some action of the overall system, then one can…
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…
A sound and complete embedding of conditional logics into classical higher-order logic is presented. This embedding enables the application of off-the-shelf higher-order automated theorem provers and model finders for reasoning within and…
Logics with team semantics provide alternative means for logical characterization of complexity classes. Both dependence and independence logic are known to capture non-deterministic polynomial time, and the frontiers of tractability in…
This work contributes to the theory of judgment aggregation by discussing a number of significant non-classical logics. After adapting the standard framework of judgment aggregation to cope with non-classical logics, we discuss in…
Recently, Logic Explained Networks (LENs) have been proposed as explainable-by-design neural models providing logic explanations for their predictions. However, these models have only been applied to vision and tabular data, and they mostly…
Higher-order functions and imperative states are language features supported by many mainstream languages. Their combination is expressive and useful, but complicates specification and reasoning, due to the use of yet-to-be-instantiated…
We develop foundational aspects of stability theory in affine logic. On the one hand, we prove appropriate affine versions of many classical results, including definability of types, existence of non-forking extensions, and other…
Federated learning enables training on a massive number of edge devices. To improve flexibility and scalability, we propose a new asynchronous federated optimization algorithm. We prove that the proposed approach has near-linear convergence…
The problem of determining the (least) fixpoint of (higher-dimensional) functions over the non-negative reals frequently occurs when dealing with systems endowed with a quantitative semantics. We focus on the situation in which the…
Recently, a novel fixed point operation has been introduced over certain non-monotonic functions between stratified complete lattices and used to give semantics to logic programs with negation and boolean context-free grammars. We prove…
Logic programming, as exemplified by datalog, defines the meaning of a program as its unique smallest model: the deductive closure of its inference rules. However, many problems call for an enumeration of models that vary along some set of…
We introduce a methodology and framework for expressing general preference information in logic programming under the answer set semantics. An ordered logic program is an extended logic program in which rules are named by unique terms, and…
Many complex scenarios require the coordination of agents possessing unique points of view and distinct semantic commitments. In response, standpoint logic (SL) was introduced in the context of knowledge integration, allowing one to reason…