Isabelle [2] is a theorem prover for a large class of logics. The object-logics are formalized within Isabelle’s meta-logic, which is intuitionistic higher-order logic with implication, universal quantifiers, and equality. The implication φ =⇒ ψ means ‘φ implies ψ’, and expresses logical entailment. The quantification ∧ x.φ means ‘φ is true for all x’, and expresses generality in rules and axio...

Abstract In this chapter, we lay the foundations for our enterprise. particular, explain how an information-based semantics, inquisitive semantics , allows us to interpret statements and questions in a uniform way define general notion of entailment which can occur as premises conclusions. We explore detail significance generalized entailment, showing particular that it captures special case im...

We study a natural variant of the implicational fragment of propositional logic. Its formulas are pairs of conjunctions of positive literals, related together by an implicational-like connective; the semantics of this sort of implication is defined in terms of a threshold on a conditional probability of the consequent, given the antecedent: we are dealing with what the data analysis community c...

Recognizing entailment at the lexical level is an important and commonly-addressed component in textual inference. Yet, this task has been mostly approached by simplified heuristic methods. This paper proposes an initial probabilistic modeling framework for lexical entailment, with suitable EM-based parameter estimation. Our model considers prominent entailment factors, including differences in...

Expert systems rules express relevant relations between their antecedents and their consequents. If the rules are manipulated by a logic (usually classical logic) in such a way that they give rise to new formulas with the form of rules (generated rules), these formulas may not express relevant relations between atecedents and consequents, and then become useless. We propose in this paper, a log...