相关论文: Abstract Canonical Inference

Detection and elimination of redundant clauses from propositional formulas in Conjunctive Normal Form (CNF) is a fundamental problem with numerous application domains, including AI, and has been the subject of extensive research. Moreover,…

An abstract argumentation framework is a commonly used formalism to provide a static representation of a dialogue. However, the order of enunciation of the arguments in an argumentative dialogue is very important and can affect the outcome…

We introduce a new symbolic representation based on an original generalization of counter abstraction. Unlike classical counter abstraction (used in the analysis of parameterized systems with unordered or unstructured topologies) the new…

The saturation-based reasoning methods are among the most theoretically developed ones and are used by most of the state-of-the-art first-order logic reasoners. In the last decade there was a sharp increase in performance of such systems,…

Combining a standard proof search method, such as resolution or tableaux, and rewriting is a powerful way to cut off search space in automated theorem proving, but proving the completeness of such combined methods may be challenging. It may…

We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…

Deduction is the one of the major forms of inferences and commonly used in formal logic. This kind of inference has the feature of monotonicity, which can be problematic. There are different types of inferences that are not monotonic, e.g.…

Dung's abstract argumentation theory is a widely used formalism to model conflicting information and to draw conclusions in such situations. Hereby, the knowledge is represented by so-called argumentation frameworks (AFs) and the reasoning…

We generalize the notion of proof term to the realm of transfinite reduction. Proof terms represent reductions in the first-order term format, thereby facilitating their formal analysis. We show that any transfinite reduction can be…

Argumentation is a process of evaluating and comparing a set of arguments. A way to compare them consists in using a ranking-based semantics which rank-order arguments from the most to the least acceptable ones. Recently, a number of such…

This article shows a correspondence between abstract interpretation of imperative programs and the refinement calculus: in the refinement calculus, an abstract interpretation of a program is a specification which is a function. This…

Fairness assumptions are a valuable tool when reasoning about systems. In this paper, we classify several fairness properties found in the literature and argue that most of them are too restrictive for many applications. As an alternative…

Based on an analysis of the inference rules used, we provide a characterization of the situations in which classical provability entails intuitionistic provability. We then examine the relationship of these derivability notions to uniform…

We present a first-order theorem proving framework for establishing the correctness of functional programs implementing sorting algorithms with recursive data structures. We formalize the semantics of recursive programs in many-sorted…

In this paper, we address the problem of change in an abstract argumentation system. We focus on a particular change: the addition of a new argument which interacts with previous arguments. We study the impact of such an addition on the…

The combination of argumentation and probability paves the way to new accounts of qualitative and quantitative uncertainty, thereby offering new theoretical and applicative opportunities. Due to a variety of interests, probabilistic…

We introduce a new covering property, defined in terms of order types of sequences of open sets, rather than in terms of cardinalities of families. The most general form of this compactness notion depends on two ordinal parameters. In the…

Abstract argumentation frameworks (AFs) provide a formal setting to analyze many forms of reasoning with conflicting information. While the expressiveness of general infinite AFs make them a tempting tool for modeling many kinds of…

After surveying classical results, we introduce a generalized notion of inference system to support structural recursion on non-well-founded data types. Besides axioms and inference rules with the usual meaning, a generalized inference…

We carry out a proof theoretic analysis of the wellfoundedness of recursive path orders in an abstract setting. We outline a very general termination principle and extract from its wellfoundedness proof subrecursive bounds on the size of…