Related papers: Synthesizing Strongly Equivalent Logic Programs: B…
We try to bring to light some combinatorial structure underlying formal proofs in logic. We do this through the study of the Craig Interpolation Theorem which is properly a statement about the structure of formal derivations. We show that…
Refinement transforms an abstract system model into a concrete, executable program, such that properties established for the abstract model carry over to the concrete implementation. Refinement has been used successfully in the development…
An approach to the revision of logic programs under the answer set semantics is presented. For programs P and Q, the goal is to determine the answer sets that correspond to the revision of P by Q, denoted P * Q. A fundamental principle of…
Epistemic Logic Programs (ELPs), that is, Answer Set Programming (ASP) extended with epistemic operators, have received renewed interest in recent years, which led to a flurry of new research, as well as efficient solvers. An important…
We propose trace logic, an instance of many-sorted first-order logic, to automate the partial correctness verification of programs containing loops. Trace logic generalizes semantics of program locations and captures loop semantics by…
We study first-order model checking, by which we refer to the problem of deciding whether or not a given first-order sentence is satisfied by a given finite structure. In particular, we aim to understand on which sets of sentences this…
Program correctness (in imperative and functional programming) splits in logic programming into correctness and completeness. Completeness means that a program produces all the answers required by its specification. Little work has been…
Over the past decade a considerable amount of research has been done to expand logic programming languages to handle incomplete information. One such language is the language of epistemic specifications. As is usual with logic programming…
This paper develops a declarative language, P-log, that combines logical and probabilistic arguments in its reasoning. Answer Set Prolog is used as the logical foundation, while causal Bayes nets serve as a probabilistic foundation. We give…
It is well-known that the verification of partial correctness properties of imperative programs can be reduced to the satisfiability problem for constrained Horn clauses (CHCs). However, state-of-the-art solvers for CHCs (CHC solvers) based…
General program equivalence is undecidable. However, if we abstract away the semantics of statements, then this problem becomes not just decidable, but practically feasible. For instance, a program of the form "if $b$ then $e$ else $f$"…
Recently, C-Log was introduced as a language for modelling causal processes. Its formal semantics has been defined together with introductory examples, but the study of this language is far from finished. In this paper, we compare C-Log to…
We present a variation of Maehara's method to construct Craig-Lyndon interpolants for the three-valued propositional logic of here and there (HT), also known as G\"odel's $G_3$, a superintuitionistic logic of importance in logic…
We show that a partial-correctness assertion about an iterative program is provable in Hoare Logic iffit is provable in standard second-order logic with comprehension restricted to first-order predicates. This equivalence was claimed twice…
A grammar formalism based upon CHR is proposed analogously to the way Definite Clause Grammars are defined and implemented on top of Prolog. These grammars execute as robust bottom-up parsers with an inherent treatment of ambiguity and a…
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…
We present a novel and well automatable approach to formal verification of programs with underspecified semantics, i.e., a language semantics that leaves open the order of certain evaluations. First, we reduce this problem to…
We propose an interpretation of the first-order answer set programming (FOASP) in terms of intuitionistic proof theory. It is obtained by two polynomial translations between FOASP and the bounded-arity fragment of the Sigma_1 level of the…
We look at characterizing which formulas are expressible in rich decidable logics such as guarded fixpoint logic, unary negation fixpoint logic, and guarded negation fixpoint logic. We consider semantic characterizations of definability, as…
In classical logic, nonBoolean fluents, such as the location of an object, can be naturally described by functions. However, this is not the case in answer set programs, where the values of functions are pre-defined, and nonmonotonicity of…