Related papers: Truth versus information in logic programming
This paper describes a simpler way for programmers to reason about the correctness of their code. The study of semantics of logic programs has shown strong links between the model theoretic semantics (truth and falsity of atoms in the…
The four-valued semantics of Belnap--Dunn logic, consisting of the truth values True, False, Neither, and Both, gives rise to several non-classical logics depending on which feature of propositions we wish to preserve: truth, non-falsity,…
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…
Types in logic programming have focused on conservative approximations of program semantics by regular types, on one hand, and on type systems based on a prescriptive semantics defined for typed programs, on the other. In this paper, we…
Bilattices provide an algebraic tool with which to model simultaneously knowledge and truth. They were introduced by Belnap in 1977 in a paper entitled \emph{How a computer should think}. Belnap argued that instead of using a logic with two…
We address the problem of integrating information coming from different sources. The information consists of facts that a central server collects and tries to combine using (a) a set of logical rules, i.e. a logic program, and (b) a…
We advocate a declarative approach to proving properties of logic programs. Total correctness can be separated into correctness, completeness and clean termination; the latter includes non-floundering. Only clean termination depends on the…
The main aim of this paper is to introduce the logics of evidence and truth LETK+ and LETF+ together with a sound, complete, and decidable six-valued deterministic semantics for them. These logics extend the logics LETK and LETF- with rules…
We define a novel, extensional, three-valued semantics for higher-order logic programs with negation. The new semantics is based on interpreting the types of the source language as three-valued Fitting-monotonic functions at all levels of…
Partial correctness of imperative or functional programming divides in logic programming into two notions. Correctness means that all answers of the program are compatible with the specification. Completeness means that the program produces…
We introduce a variant of free logic (i.e., a logic admitting terms with nonexistent referents) that accommodates truth-value gluts as well as gaps. Employing a suitable expansion of the Belnap-Dunn four-valued logic, we specify a…
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…
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…
The paper introduces fuzzy linguistic logic programming, which is a combination of fuzzy logic programming, introduced by P. Vojtas, and hedge algebras in order to facilitate the representation and reasoning on human knowledge expressed in…
Prioritized default reasoning has illustrated its rich expressiveness and flexibility in knowledge representation and reasoning. However, many important aspects of prioritized default reasoning have yet to be thoroughly explored. In this…
\textbf{T-BAT} logic is a formal system designed to express the notion of informal provability. This type of provability is closely related to mathematical practice and is quite often contrasted with formal provability, understood as a…
We describe an approach for compiling preferences into logic programs under the answer set semantics. An ordered logic program is an extended logic program in which rules are named by unique terms, and in which preferences among rules are…
Real-valued logics underlie an increasing number of neuro-symbolic approaches, though typically their logical inference capabilities are characterized only qualitatively. We provide foundations for establishing the correctness and power of…
Convincing someone of the truth value of a premise requires understanding and articulating the core logical structure of the argument which proves or disproves the premise. Understanding the logical structure of an argument refers to…
In this work we present additional results related to the property of strong equivalence of logic programs. This property asserts that two programs share the same set of stable models, even under the addition of new rules. As shown in a…