Towards a unified theory of intensional logic programming

AbstractIntensional Logic Programming is a new form of logic programming based on intensional logic and possible worlds semantics. Intensional logic allows us to use logic programming to specify nonterminating computations and to capture the dynamic aspects of certain problems in a natural and problem-oriented style. The meanings of formulas of an intensional first-order language are given according to intensional interpretations and to elements of a set of possible worlds. Neighborhood semantics is employed as an abstract formulation of the denotations of intensional operators. Then we investigate general properties of intensional operators such as universality, monotonicity, finitariness and conjunctivity. These properties are used as constraints on intensional logic programming systems. The model-theoretic and fixpoint semantics of intensional logic programs are developed in terms of least (minimum) intensional Herbrand models. We show in particular that our results apply to a number of intensional logic programming languages such as Chronolog proposed by Wadge and Templog by Abadi and Manna. We consider some elementary extensions to the theory and show that intensional logic program clauses can be used to define new intensional operators. Intensional logic programs with intensional operator definitions are regarded as metatheories

A Coalgebraic Perspective on Probabilistic Logic Programming

Probabilistic logic programming is increasingly important in artificial intelligence and related fields as a formalism to reason about uncertainty. It generalises logic programming with the possibility of annotating clauses with probabilities. This paper proposes a coalgebraic perspective on probabilistic logic programming. Programs are modelled as coalgebras for a certain functor F, and two semantics are given in terms of cofree coalgebras. First, the cofree F-coalgebra yields a semantics in terms of derivation trees. Second, by embedding F into another type G, as cofree G-coalgebra we obtain a "possible worlds" interpretation of programs, from which one may recover the usual distribution semantics of probabilistic logic programming

Coalgebraic Semantics for Probabilistic Logic Programming

Probabilistic logic programming is increasingly important in artificial intelligence and related fields as a formalism to reason about uncertainty. It generalises logic programming with the possibility of annotating clauses with probabilities. This paper proposes a coalgebraic semantics on probabilistic logic programming. Programs are modelled as coalgebras for a certain functor F, and two semantics are given in terms of cofree coalgebras. First, the F-coalgebra yields a semantics in terms of derivation trees. Second, by embedding F into another type G, as cofree G-coalgebra we obtain a `possible worlds' interpretation of programs, from which one may recover the usual distribution semantics of probabilistic logic programming. Furthermore, we show that a similar approach can be used to provide a coalgebraic semantics to weighted logic programming

Coalgebraic semantics for probabilistic logic programming

Probabilistic logic programming is increasingly important in artificial intelligence and related fields as a formalism to reason about uncertainty. It generalises logic programming with the possibility of annotating clauses with probabilities. This paper proposes a coalgebraic semantics on probabilistic logic programming. Programs are modelled as coalgebras for a certain functor F, and two semantics are given in terms of cofree coalgebras. First, the cofree F-coalgebra yields a semantics in terms of derivation trees. Second, by embedding F into another type G, as cofree G-coalgebra we obtain a 'possible worlds' interpretation of programs, from which one may recover the usual distribution semantics of probabilistic logic programming. Furthermore, we show that a similar approach can be used to provide a coalgebraic semantics to weighted logic programming

A coalgebraic perspective on probabilistic logic programming

Probabilistic logic programming is increasingly important in artificial intelligence and related fields as a formalism to reason about uncertainty. It generalises logic programming with the possibility of annotating clauses with probabilities. This paper proposes a coalgebraic perspective on probabilistic logic programming. Programs are modelled as coalgebras for a certain functor F, and two semantics are given in terms of cofree coalgebras. First, the cofree F-coalgebra yields a semantics in terms of derivation trees. Second, by embedding F into another type G, as cofree G-coalgebra we obtain a “possible worlds” interpretation of programs, from which one may recover the usual distribution semantics of probabilistic logic programming

UTP2: Higher-Order Equational Reasoning by Pointing

We describe a prototype theorem prover, UTP2, developed to match the style of hand-written proof work in the Unifying Theories of Programming semantical framework. This is based on alphabetised predicates in a 2nd-order logic, with a strong emphasis on equational reasoning. We present here an overview of the user-interface of this prover, which was developed from the outset using a point-and-click approach. We contrast this with the command-line paradigm that continues to dominate the mainstream theorem provers, and raises the question: can we have the best of both worlds?Comment: In Proceedings UITP 2014, arXiv:1410.785