A Proof-Based Annotation Platform of Textual Entailment

We introduce a new platform for annotating inferential phenomena in entailment data, buttressed by a formal semantic model and a proof-system that provide immediate verification of the coherency and completeness of the marked annotations. By integrating a web-based user interface, a formal lexicon, a lambda-calculus engine and an off-the-shelf theorem prover, the platform allows human annotators to mark linguistic phenomena in entailment data (pairs made up of a premise and a hypothesis) and to receive immediate feedback whether their annotations are substantiated: for positive entailment pairs, the system searches for a formal logical proof that the hypothesis follows from the premise; for negative pairs, the system verifies that a counter-model can be constructed. This novel approach facilitates the creation of textual entailment corpora with annotations that are sufficiently coherent and complete for recognizing the entailment relation or lack thereof. A corpus of several hundred annotated entailments is currently being compiled based on the platform and will be available for the research community in the foreseeable future

An interactive approach to proof-theoretic semantics

In truth-functional semantics for propositional logics, categoricity and compositionality are unproblematic. This is not the case for proof-theoretic semantics, where failures of both occur for the semantics determined by monological entailment structures for classical and intuitionistic logic. This is problematic for inferentialists, where the meaning of logical constants is supposed to be determined by their rules. Recent attempts to overcome these issues have primarily considered symmetric entailment structures, but these are tricky to interpret. Here, I instead consider an entailment structure that combines provability with the dual notion of disproof (or refutation). This is interpreted as a dialogue structure between the roles of prover and denier, where an assertion of a statement involves a commitment to its defence, and a denial of the statement involves a commitment to its challenge. The interaction between the two is constitutive of a proof-theoretic semantics capable of dealing with the above issues

Measuring the understandability of deduction rules for OWL

Debugging OWL ontologies can be aided with automated reasoners that generate entailments, including undesirable ones. This information is, however, only useful if developers understand why the entailments hold. To support domain experts (with limited knowledge of OWL), we are developing a system that explains, in English, why an entailment follows from an ontology. In planning such explanations, our system starts from a justification of the entailment and constructs a proof tree including intermediate statements that link the justification to the entailment. Proof trees are constructed from a set of intuitively plausible deduction rules. We here report on a study in which we collected empirical frequency data on the understandability of the deduction rules, resulting in a facility index for each rule. This measure forms the basis for making a principled choice among alternative explanations, and identifying steps in the explanation that are likely to require extra elucidation