Related papers: Well structured program equivalence is highly unde…
A new approach to the design of massively parallel and interactive programming languages has been recently proposed using rv-systems (interactive systems with registers and voices) and Agapia programming. In this paper we present a few…
We present realizability and realization logic, two program logics that jointly address the problem of finding solutions in semantics-guided synthesis. What is new is that we proceed eagerly and not only analyze a single candidate program…
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…
We study the axiomatisability of the iteration-free fragment of Propositional Dynamic Logic with Intersection and Tests. The combination of program composition, intersection and tests makes its proof-theory rather difficult. We develop a…
Logics for knowledge representation suffer from over-specialization: while each logic may provide an ideal representation formalism for some problems, it is less than optimal for others. A solution to this problem is to choose from several…
The classical propositional logic is known to be sound and complete with respect to the set semantics that interprets connectives as set operations. The paper extends propositional language by a new binary modality that corresponds to…
We propose a presentation of classical propositional tableaux elaborated by application of methods that are noteworthy in program design, namely program derivation with separation of concerns. We start by deriving from a straightforward…
In the same sense as classical logic is a formal theory of truth, the recently initiated approach called computability logic is a formal theory of computability. It understands (interactive) computational problems as games played by a…
Transductions are binary relations of finite words. For rational transductions, i.e., transductions defined by finite transducers, the inclusion, equivalence and sequential uniformisation problems are known to be undecidable. In this paper,…
A probabilistic propositional logic, endowed with an epistemic component for asserting (non-)compatibility of diagonizable and bounded observables, is presented and illustrated for reasoning about the random results of projective…
We investigate the decidability of the definability problem for fragments of first order logic over finite words enriched with modular predicates. Our approach aims toward the most generic statements that we could achieve, which…
In this paper, we consider the satisfiability problem for string logic with equations, regular membership and Presburger constraints over length functions. The difficulty comes from multiple occurrences of string variables making…
We systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted…
We introduce a generalized logic programming paradigm where programs, consisting of facts and rules with the usual syntax, can be enriched by co-facts, which syntactically resemble facts but have a special meaning. As in coinductive logic…
Computer programs may go wrong due to exceptional behaviors, out-of-bound array accesses, or simply coding errors. Thus, they cannot be blindly trusted. Scientific computing programs make no exception in that respect, and even bring…
While modal extensions of decidable fragments of first-order logic are usually undecidable, their monodic counterparts, in which formulas in the scope of modal operators have at most one free variable, are typically decidable. This only…
Relying on the formulae-as-types paradigm for classical logic, we define a program logic for an imperative language with higher-order procedural variables and non-local jumps. Then, we show how to derive a sound program logic for this…
Stable Logic Programming (SLP) is an emergent, alternative style of logic programming: each solution to a problem is represented by a stable model of a deductive database/function-free logic program encoding the problem itself. Several…
A non-deterministic recursion scheme recognizes a language of finite trees. This very expressive model can simulate, among others, higher-order pushdown automata with collapse. We show decidability of the diagonal problem for schemes. This…
We consider decision problems for relations over finite and infinite words defined by finite automata. We prove that the equivalence problem for binary deterministic rational relations over infinite words is undecidable in contrast to the…