Related papers: A type system for PSPACE derived from light linear…
Functional logic programming (FLP) languages use non-terminating and non-confluent constructor systems (CS's) as programs in order to define non-strict non-determi-nistic functions. Two semantic alternatives have been usually considered for…
Girard's Light linear logic (LLL) characterized polynomial time in the proof-as-program paradigm with a bound on cut elimination. This logic relied on a stratification principle and a "one-door" principle which were generalized later…
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…
Over the past three decades, the logic programming paradigm has been successfully expanded to support probabilistic modeling, inference and learning. The resulting paradigm of probabilistic logic programming (PLP) and its programming…
We introduce an implementation of an extension of Answer Set Programming (ASP) with language constructs from dynamic (and temporal) logic that provides an expressive computational framework for modeling dynamic applications. Starting from…
This paper shows the debugging facilities provided by the SLAM system. The SLAM system includes i) a specification language that integrates algebraic specifications and model-based specifications using the object oriented model. Class…
Lambda Prolog is known to be well-suited for expressing and implementing logics and inference systems. We show that lemmas and definitions in such logics can be implemented with a great economy of expression. We encode a higher-order logic…
Type inference is an application domain that is a natural fit for logic programming (LP). LP systems natively support unification, which serves as a basic building block of typical type inference algorithms. In particular, polymorphic type…
We present the guarded lambda-calculus, an extension of the simply typed lambda-calculus with guarded recursive and coinductive types. The use of guarded recursive types ensures the productivity of well-typed programs. Guarded recursive…
Dynamic logic is a powerful approach to reasoning about programs and their executions, obtained by extending classical logic with modalities that can express program executions as formulas. However, the use of dynamic logic in the setting…
Provability logics are modal or polymodal systems designed for modeling the behavior of G\"odel's provability predicate in arithmetical theories and its natural extensions. If \Lambda is any ordinal, the G\"odel-L\"ob calculus GLP(\Lambda)…
Learning rules plays a crucial role in deep learning, particularly in explainable artificial intelligence and enhancing the reasoning capabilities of large language models. While existing rule learning methods are primarily designed for…
The paper describes two iterative algorithms for solving general systems of M simultaneous linear algebraic equations (SLAE) with real matrices of coefficients. The system can be determined, underdetermined, and overdetermined. Linearly…
In this paper we elaborate on a specific application in the context of hybrid description logic programs (hybrid DLPs), namely description logic Semantic Web type systems (DL-types) which are used for term typing of LP rules based on a…
We prove that the sequent calculus $\mathsf{L_{RBL}}$ for residuated basic logic $\mathsf{RBL}$ has strong finite model property, and that intuitionistic logic can be embedded into basic propositional logic $\mathsf{BPL}$. Thus…
We consider the non-deterministic extension of the call-by-value lambda calculus, which corresponds to the additive fragment of the linear-algebraic lambda-calculus. We define a fine-grained type system, capturing the right linearity…
Answer Set Programming (ASP), a well-known declarative logic programming paradigm, has recently found practical application in Process Mining. In particular, ASP has been used to model tasks involving declarative specifications of business…
We present a typed computer language, Doug, in which all typed programs may be proved to halt in polynomial time, encoded in a vector-symbolic architecture (VSA). Doug is just an encoding of the light linear functional programming language…
The Dynamic Logic for Propositional Assignments (DL-PA) has recently been studied as an alternative to Propositional Dynamic Logic (PDL). In DL-PA, the abstract atomic programs of PDL are replaced by assignments of propositional variables…
We present a tableau-based algorithm for deciding satisfiability for propositional dynamic logic (PDL) which builds a finite rooted tree with ancestor loops and passes extra information from children to parents to separate good loops from…