We study a logical system FQHT that is appropriate for reasoning about nonmonotonic theories with intensional functions as treated in the approach of [Bartholomew and Lee, 2012]. We provide a logical semantics, a Gentzen style proof theory and establish completeness results. The adequacy of the approach is demonstrated by showing that it captures the Bartholemew/Lee semantics and satisfies a st...

Metareasoning can be achieved in probabilistic programming languages (PPLs) using agent models that recursively nest inference queries inside queries. However, the semantics of this powerful, reflection-like language feature has defied an operational treatment, much less reasoning principles for contextual equivalence. We give formal to a core PPL with continuous distributions, scoring, general...

We present a new semantics for Description Logic programs [1] (dlprograms) that combine reasoning about ontologies in description logics with non-monotonic rules interpreted under answer set semantics. Our semantics is equivalent to that of [1], but is more logical in style, being based on the logic QHT of quantified here-and-there that provides a foundation for ordinary logic programs under an...

The paper presents an approach for handling uncertain information in deductive databases using multivalued logics. Uncertainty means that database facts may be assigned logical values other than the conventional ones true and false. The logical values represent various degrees of truth, which may be combined and propagated by applying the database rules. A corresponding multivalued database sem...

We present n-valued rst-order logics with a purely proba-bilistic semantics. We then introduce a new probabilistic semantics of n-valued rst-order logics that lies between the purely probabilistic semantics and the truth-functional semantics of the n-valued Lukasiewicz logics Ln. Within this semantics, closed formulas of classical rst-order logics that are logically equivalent in the classical ...

Suppose we want to build a system that answers a natural language question by representing its semantics as a logical form and computing the answer given a structured database of facts. The core part of such a system is the semantic parser that maps questions to logical forms. Semantic parsers are typically trained from examples of questions annotated with their target logical forms, but this t...

Abstract dialectical frameworks (ADFs) have been introduced as a formalism for modeling argumentation allowing general logical satisfaction conditions and the relevant argument evaluation. Different criteria used to settle acceptance of arguments are called semantics. Semantics ADFs so far mainly defined based on concept admissibility. However, notion strongly admissible semantics studied abstr...

Thom Fr\"uhwirth presented a short, elegant and efficient Prolog program for the n queens problem. However may be seen as rather tricky one not convinced about its correctness. This paper explains in declarative way, provides proofs of correctness completeness. The specification are declarative, i.e. they abstract from any operational semantics. is approximate, it unnecessary to describe progra...

This thesis proposes a generalisation of pre-logical predicates to simply typed formal systems and their categorical models. We analyse the three elements involved in pre-logical predicates — syntax, semantics and predicates — within a categorical framework for typed binding syntax and semantics. We then formulate generalised pre-logical predicates and show two distinguishing properties: a) equ...

Of the common commutative binary logical connectives, only and and ormay be used as operators that take arbitrary numbers of arguments with order and multiplicity being irrelevant, that is, as connectives that take sets of arguments. This is especially evident in the Common Logic Interchange Format, in which it is easy for operators to be given arbitrary numbers of arguments. The reason is that...