Related papers: Here and There with Arithmetic
Answer-set programming (ASP) paradigm is a way of using logic to solve search problems. Given a search problem, to solve it one designs a theory in the logic so that models of this theory represent problem solutions. To compute a solution…
Answer set programming (ASP) is a well-established logic programming language that offers an intuitive, declarative syntax for problem solving. In its traditional application, a fixed ASP program for a given problem is designed and the…
We show a projective Beth definability theorem for logic programs under the stable model semantics: For given programs $P$ and $Q$ and vocabulary $V$ (set of predicates) the existence of a program $R$ in $V$ such that $P \cup R$ and $P \cup…
Answer Set Programming (ASP) is a prominent rule-based language for knowledge representation and reasoning with roots in logic programming and non-monotonic reasoning. The aim to capture the essence of removing (ir)relevant details in ASP…
Two distinct research approaches have been proposed for assigning a purely extensional semantics to higher-order logic programming. The former approach uses classical domain theoretic tools while the latter builds on a fixed-point…
We target the problem of provably computing the equivalence between two complex expression trees. To this end, we formalize the problem of equivalence between two such programs as finding a set of semantics-preserving rewrite rules from one…
Strong equivalence is a well-studied and important concept in answer set programming (ASP). $\rm LP^{MLN}$ is a probabilistic extension of answer set programs with the weight scheme adapted from Markov Logic. Because of the semantic…
We introduce the framework of qualitative optimization problems (or, simply, optimization problems) to represent preference theories. The formalism uses separate modules to describe the space of outcomes to be compared (the generator) and…
A logic program is an executable specification. For example, merge sort in pure Prolog is a logical formula, yet shows creditable performance on long linked lists. But such executable specifications are a compromise: the logic is distorted…
We take up an idea from the folklore of Answer Set Programming, namely that choices, integrity constraints along with a restricted rule format is sufficient for Answer Set Programming. We elaborate upon the foundations of this idea in the…
In Pure Inductive Logic, the principle of Strong Predicate Exchangeability is a rational principle based on symmetry that sits in between the principles of Predicate Exchangeability and Atom Exchangeability. We will show a de Finetti -…
We show that strict deterministic propositional dynamic logic with intersection is highly undecidable, solving a problem in the Stanford Encyclopedia of Philosophy. In fact we show something quite a bit stronger. We introduce the…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
This paper presents matching logic, a first-order logic (FOL) variant for specifying and reasoning about structure by means of patterns and pattern matching. Its sentences, the patterns, are constructed using variables, symbols, connectives…
We provide here a computational interpretation of first-order logic based on a constructive interpretation of satisfiability w.r.t. a fixed but arbitrary interpretation. In this approach the formulas themselves are programs. This contrasts…
This paper aims to provide an analysis of what it means when we say that a pair of theories, very generously construed, are equivalent in the sense that they are interdefinable. With regard to theories articulated in first order logic, we…
Interpolation is an important property of classical and many non-classical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the the non-monotonic system of…
The Curry-Howard correspondence is about a relationship between types and programs on the one hand and propositions and proofs on the other. The implications for programming language design and program verification is an active field of…
A correspondence is established between the elements of logic reasoning systems (knowledge bases, rules, inference and queries) and the hardware and dynamical operations of neural networks. The correspondence is framed as a general…
In the same sense as classical logic is a formal theory of truth, the recently initiated approach called computability logic is a formal theory of computability. It understands (interactive) computational problems as games played by a…