Related papers: Normal forms for Answer Sets Programming
The different semantics that can be assigned to a logic program correspond to different assumptions made concerning the atoms whose logical values cannot be inferred from the rules. Thus, the well founded semantics corresponds to the…
Modern answer set programming solvers such as CLINGO support advanced language constructs that improve the expressivity and conciseness of logic programs. Conditional literals are one such construct. They form "subformulas" that behave as…
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…
The paper describes an extension of well-founded semantics for logic programs with two types of negation. In this extension information about preferences between rules can be expressed in the logical language and derived dynamically. This…
Formal deductive systems are very common in computer science. They are used to represent logics, programming languages, and security systems. Moreover, writing programs that manipulate them and that reason about them is important and…
Many logic programming based approaches can be used to describe and solve combinatorial search problems. On the one hand there are definite programs and constraint logic programs that compute a solution as an answer substitution to a query…
Answer Set Programming (ASP) is a well-established formalism for nonmonotonic reasoning. An ASP program can have no answer set due to cyclic default negation. In this case, it is not possible to draw any conclusion, even if this is not…
Semantics of logic programs has been given by proof theory, model theory and by fixpoint of the immediate-consequence operator. If clausal logic is a programming language, then it should also have a compositional semantics. Compositional…
This paper contributes to the mathematical foundations of logic programming by introducing and studying the sequential composition of answer set programs. On the semantic side, we show that the immediate consequence operator of a program…
In the context of the Semantic Web, several approaches to the combination of ontologies, given in terms of theories of classical first-order logic and rule bases, have been proposed. They either cast rules into classical logic or limit the…
A re-construction of the fundamentals of programming as a small mathematical theory (PRISM) based on elementary set theory. Highlights: $\bullet$ Zero axioms. No properties are assumed, all are proved (from standard set theory). $\bullet$ A…
In this note, we use Kunen's notion of a signing to establish two theorems about the well-founded semantics of logic programs, in the case where we are interested in only (say) the positive literals of a predicate $p$ that are consequences…
Digraphs provide an alternative syntax for propositional logic, with digraph kernels corresponding to classical models. Semikernels generalize kernels and we identify a subset of well-behaved semikernels that provides nontrivial models for…
In traditional software programs, it is easy to trace program logic from variables back to input, apply assertion statements to block erroneous behavior, and compose programs together. Although deep learning programs have demonstrated…
In functional logic programs, rules are applicable independently of textual order, i.e., any rule can potentially be used to evaluate an expression. This is similar to logic languages and contrary to functional languages, e.g., Haskell…
Structural equation models (SEMs) have been widely adopted for inference of causal interactions in complex networks. Recent examples include unveiling topologies of hidden causal networks over which processes such as spreading diseases, or…
An object--oriented approach to create a natural language understanding system is considered. The understanding program is a formal system built on the base of predicative calculus. Horn's clauses are used as well--formed formulas. An…
We present an extension of Logic Programming (under stable models semantics) that, not only allows concluding whether a true atom is a cause of another atom, but also deriving new conclusions from these causal-effect relations. This is…
Applying dynamic logics to program verifications is a challenge, because their axiomatic rules for regular expressions can be difficult to be adapted to different program models. We present a novel dynamic logic, called DLp, which supports…
Programming with logic for sophisticated applications must deal with recursion and negation, which together have created significant challenges in logic, leading to many different, conflicting semantics of rules. This paper describes a…