Related papers: A Logical Study of Partial Entailment
Two results are presented concerning the entailment problem in Separation Logic with inductively defined predicate symbols and theory reasoning. First, we show that the entailment problem is undecidable for rules with bounded tree-width, if…
We consider the problem of answering queries about formulas of propositional logic based on background knowledge partially represented explicitly as other formulas, and partially represented as partially obscured examples independently…
We involve a certain propositional logic based on ortholattices. We characterize the implicational reduct of such a logic and we show that its algebraic counterpart is the so-called orthosemilattice. Properties of congruences and congruence…
We propose a combination of probabilistic reasoning from conditional constraints with approaches to default reasoning from conditional knowledge bases. In detail, we generalize the notions of Pearl's entailment in system Z, Lehmann's…
The term proposition usually denotes in quantum mechanics (QM) an element of (standard) quantum logic (QL). Within the orthodox interpretation of QM the propositions of QL cannot be associated with sentences of a language stating properties…
In this paper we put forward a new solution of the well-known problem of relevant logics, i.e. we construct an atomic entailment. Hence, we construct a system of predicate calculus based on the atomic entailment. Next, we establish the…
Epistemic logic programs constitute an extension of the stable models semantics to deal with new constructs called subjective literals. Informally speaking, a subjective literal allows checking whether some regular literal is true in all…
Logical reasoning is central to human cognition and intelligence. It includes deductive, inductive, and abductive reasoning. Past research of logical reasoning within AI uses formal language as knowledge representation and symbolic…
We introduce a logical framework for reasoning about "uncertain interpretations" and investigate two key applications: a new semantics for implication capturing a kind of "meaning entailment", and a conservative notion of "evidentially…
We survey the different properties of an intuitive notion of redundancy, as a function of the precise semantics given to the notion of partial implication. The final version of this survey will appear in the Proceedings of the Int. Conf.…
The frame of classical probability theory can be generalized by enlarging the usual family of random variables in order to encompass nondeterministic ones: this leads to a frame in which two kinds of correlations emerge: the classical…
The entailment between separation logic formulae with inductive predicates, also known as symbolic heaps, has been shown to be decidable for a large class of inductive definitions. Recently, a 2-EXPTIME algorithm was proposed and an…
The quantum-mechanical description of the world, including human observers, makes substantial use of entanglement. In order to understand this, we need to adopt concepts of truth, probability and time which are unfamiliar in modern…
The Logic of Approximate Entailment (LAE) is a graded counterpart of classical propositional calculus, where conclusions that are only approximately correct can be drawn. This is achieved by equipping the underlying set of possible worlds…
We investigate the problem of learning description logic ontologies from entailments via queries, using epistemic reasoning. We introduce a new learning model consisting of epistemic membership and example queries and show that polynomial…
This paper explores the space of (propositional) probabilistic logical languages, ranging from a purely `qualitative' comparative language to a highly `quantitative' language involving arbitrary polynomials over probability terms. While…
In this paper, we introduce a new type of $ pq $-calculus. The $ pq $-derivative and $ pq $-integration are investigated and various properties of these concepts are given. The fundamental theorem of $ pq $-calculus and formulas of $ pq…
In this paper, we present an alternative interpretation of propositional inquisitive logic as an epistemic logic of knowing how. In our setting, an inquisitive logic formula $\alpha$ being supported by a state is formalized as "knowing how…
We provide a Lawvere-style definition for partial theories, extending the classical notion of equational theory by allowing partially defined operations. As in the classical case, our definition is syntactic: we use an appropriate class of…
There has been a growing interest in explaining entailments over description logic (DL) knowledge bases. The existing explanation formalisms focus on justifications to explain true axioms, and abductive reasoning to explain missing axioms…