Related papers: Sequential decomposition of propositional logic pr…
Part of the theory of logic programming and nonmonotonic reasoning concerns the study of fixed-point semantics for these paradigms. Several different semantics have been proposed during the last two decades, and some have been more…
It is well known that, under certain conditions, it is possible to split logic programs under stable model semantics, i.e. to divide such a program into a number of different "levels", such that the models of the entire program can be…
Propositional Dynamic Logic, PDL, is a modal logic designed to formalize the reasoning about programs. By extending accessibility between states to states and state sets, concurrent propositional dynamic logic CPDL, is introduced to include…
We study algebraic properties of the semigroup $\mathscr{O\!\!I\!}_n(L)$ of finite partial order isomorphisms of the rank $\leq n$ of an infinite linearly ordered set $(L,\leqslant)$. In particular we describe its idempotents, the natural…
This paper proposes new derivations of three well-known sorting algorithms, in their functional formulation. The approach we use is based on three main ingredients: first, the algorithms are derived from a simpler algorithm, i.e. the…
The work is devoted to Computability Logic (CoL) -- the philosophical/mathematical platform and long-term project for redeveloping classical logic after replacing truth} by computability in its underlying semantics (see…
This paper introduces a new kind of propositional encoding for reasoning about partial orders. The symbols in an unspecified partial order are viewed as variables which take integer values and are interpreted as indices in the order. For a…
A major bottleneck in search-based program synthesis is the exponentially growing search space which makes learning large programs intractable. Humans mitigate this problem by leveraging the compositional nature of the real world: In…
This paper describes a general framework for automatic termination analysis of logic programs, where we understand by ``termination'' the finitenes s of the LD-tree constructed for the program and a given query. A general property of…
We discuss the application of random projections to conic programming: notably linear, second-order and semidefinite programs. We prove general approximation results on feasibility and optimality using the framework of formally real Jordan…
Termination of logic programs depends critically on the selection rule, i.e. the rule that determines which atom is selected in each resolution step. In this article, we classify programs (and queries) according to the selection rules for…
This paper presents State Algebra, a novel framework designed to represent and manipulate propositional logic using algebraic methods. The framework is structured as a hierarchy of three representations: Set, Coordinate, and Row…
Using a variant of Schreier's Theorem, and the theory of Green's relations, we show how to reduce the computation of an arbitrary subsemigroup of a finite regular semigroup to that of certain associated subgroups. Examples of semigroups to…
$\{log\}$ is a programming language at the intersection of Constraint Logic Programming, set programming and declarative programming. But $\{log\}$ is also a satisfiability solver for a theory of finite sets and finite binary relations.…
In this paper we present algorithmic considerations and theoretical results about the relation between the orders of certain groups associated to the components of a polynomial and the order of the group that corresponds to the polynomial,…
Inspired by the theory of poset games, we introduce a new compound of impartial combinatorial games and provide a complete analysis in the spirit of the Sprague-Grundy theory. Furthermore, we establish several substitution and reduction…
Separation logic's compositionality and local reasoning properties have led to significant advances in scalable static analysis. But program analysis has new challenges -- many programs display computational effects and, orthogonally,…
Program equivalence in linear contexts, where programs are used or executed exactly once, is an important issue in programming languages. However, existing techniques like those based on bisimulations and logical relations only target at…
We present a novel technique for proving program termination which introduces a new dimension of modularity. Existing techniques use the program to incrementally construct a termination proof. While the proof keeps changing, the program…
Disjunctive finitary programs are a class of logic programs admitting function symbols and hence infinite domains. They have very good computational properties, for example ground queries are decidable while in the general case the stable…