Related papers: Complexity of Non-Monotonic Logics

We survey systematic approaches to basis-restricted fragments of propositional logic and modal logics, with an emphasis on how expressive power and computational complexity depend on the allowed operators. The propositional case is…

In this paper we make a contribution to the unification of formal models of defeasible reasoning. We present several translations between formal argumentation frameworks and nonmonotonic logics for reasoning with plausible assumptions. More…

Non deterministic applications arise in many domains, including, stochastic optimization, multi-objectives optimization, stochastic planning, contingent stochastic planning, reinforcement learning, reinforcement learning in partially…

Weighted monadic second-order logic is a weighted extension of monadic second-order logic that captures exactly the behaviour of weighted automata. Its semantics is parameterized with respect to a semiring on which the values that weighted…

We define a family of intuitionistic non-normal modal logics; they can bee seen as intuitionistic counterparts of classical ones. We first consider monomodal logics, which contain only one between Necessity and Possibility. We then consider…

Attempts to replicate probabilistic reasoning in expert systems have typically overlooked a critical ingredient of that process. Probabilistic analysis typically requires extensive judgments regarding interdependencies among hypotheses and…

We introduce and study logic programs whose clauses are built out of monotone constraint atoms. We show that the operational concept of the one-step provability operator generalizes to programs with monotone constraint atoms, but the…

Plausible reasoning concerns situations whose inherent lack of precision is not quantified; that is, there are no degrees or levels of precision, and hence no use of numbers like probabilities. A hopefully comprehensive set of principles…

An important endeavor in computer science is to understand the expressive power of logical formalisms over discrete structures, such as words. Naturally, "understanding" is not a mathematical notion. This investigation requires therefore a…

Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurs-check) and increased expressivity (cyclic terms can…

Recently, several approaches to updating knowledge bases modeled as extended logic programs have been introduced, ranging from basic methods to incorporate (sequences of) sets of rules into a logic program, to more elaborate methods which…

Propositional Typicality Logic (PTL) is a recently proposed logic, obtained by enriching classical propositional logic with a typicality operator capturing the most typical (alias normal or conventional) situations in which a given sentence…

We give a proof-theoretic as well as a semantic characterization of a logic in the signature with conjunction, disjunction, negation, and the universal and existential quantifiers that we suggest has a certain fundamental status. We present…

Possibilistic logic, an extension of first-order logic, deals with uncertainty that can be estimated in terms of possibility and necessity measures. Syntactically, this means that a first-order formula is equipped with a possibility degree…

State of the art algorithms for many pattern recognition problems rely on deep network models. Training these models requires a large labeled dataset and considerable computational resources. Also, it is difficult to understand the working…

Defeasible logic is a rule-based nonmonotonic logic, with both strict and defeasible rules, and a priority relation on rules. We show that inference in the propositional form of the logic can be performed in linear time. This contrasts…

This paper presents Abduction and Argumentation as two principled forms for reasoning, and fleshes out the fundamental role that they can play within Machine Learning. It reviews the state-of-the-art work over the past few decades on the…

The importance of transformations and normal forms in logic programming, and generally in computer science, is well documented. This paper investigates transformations and normal forms in the context of Defeasible Logic, a simple but…

While modal extensions of decidable fragments of first-order logic are usually undecidable, their monodic counterparts, in which formulas in the scope of modal operators have at most one free variable, are typically decidable. This only…

Traditional approaches to non-monotonic reasoning fail to satisfy a number of plausible axioms for belief revision and suffer from conceptual difficulties as well. Recent work on ranked preferential models (RPMs) promises to overcome some…