Related papers: On Answer Substitutions in Logic Programming
Predicate Logic with Definitions (PLD or D-logic) is a modification of first-order logic intended mostly for practical formalization of mathematics. The main syntactic constructs of D-logic are terms, formulas and definitions. A definition…
Plausible reasoning concerns situations whose inherent lack of precision is not quantified; that is, there are no degrees or levels of precision, and hence no use of numbers like probabilities. A hopefully comprehensive set of principles…
Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html ) is a research program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth which it has more traditionally been.…
Relying on the formulae-as-types paradigm for classical logic, we define a program logic for an imperative language with higher-order procedural variables and non-local jumps. Then, we show how to derive a sound program logic for this…
The stable model semantics had been recently generalized to non-Herbrand structures by several works, which provides a unified framework and solid logical foundations for answer set programming. This paper focuses on the expressiveness of…
Given a conditional sentence "P=>Q" (if P then Q) and respective facts, four different types of inferences are observed in human reasoning. Affirming the antecedent (AA) (or modus ponens) reasons Q from P; affirming the consequent (AC)…
An equational logic program is a set of directed equations or rules, which are used to compute in the obvious way (by replacing equals with ``simpler'' equals). We present static analysis techniques for efficient equational logic…
We consider entailment problems involving powerful constraint languages such as guarded existential rules, in which additional semantic restrictions are put on a set of distinguished relations. We consider restricting a relation to be…
Artificial Intelligence (AI) approaches to problem-solving and decision-making are becoming more and more complex, leading to a decrease in the understandability of solutions. The European Union's new General Data Protection Regulation…
We introduce the notion of contrastive ABox explanations to answer questions of the type "Why is a an instance of C, but b is not?". While there are various approaches for explaining positive entailments (why is C(a) entailed by the…
Possibilistic logic programs (poss-programs) under stable models are a major variant of answer set programming (ASP). While its semantics (possibilistic stable models) and properties have been well investigated, the problem of inductive…
This paper presents a property of propositional theories under the answer sets semantics (called Equilibrium Logic for this general syntax): any theory can always be reexpressed as a strongly equivalent disjunctive logic program, possibly…
A new type of deterministic (non-probabilistic) computer logic system inspired by the stochasticity of brain signals is shown. The distinct values are represented by independent stochastic processes: independent voltage (or current) noises.…
We introduce a variation on Barthe et al.'s higher-order logic in which formulas are interpreted as predicates over open rather than closed objects. This way, concepts which have an intrinsically functional nature, like continuity,…
We present a logical separability analysis for a functional quantum computation language. This logic is inspired by previous works on logical analysis of aliasing for imperative functional programs. Both analyses share similarities notably…
In the theory of answer set programming, two groups of rules are called strongly equivalent if, informally speaking, they have the same meaning in any context. The relationship between strong equivalence and the propositional logic of…
Computability logic is a formal theory of computational tasks and resources. Its formulas represent interactive computational problems, logical operators stand for operations on computational problems, and validity of a formula is…
The problem of giving a computational meaning to classical reasoning lies at the heart of logic. This article surveys three famous solutions to this problem - the epsilon calculus, modified realizability and the dialectica interpretation -…
We unify functional and logic programming by treating predicatesas functions equipped with their support: the set of inputs whose output is nonzero. Datalog, for instance, is a language of finitely supported boolean functions. Finite…
While explainability is a desirable characteristic of increasingly complex black-box models, modern explanation methods have been shown to be inconsistent and contradictory. The semantics of explanations is not always fully understood - to…