Related papers: A Decision Procedure for Guarded Separation Logic:…
Answering Boolean conjunctive queries over the guarded fragment is decidable, however, as yet no practical decision procedure exists. Meanwhile, ordered resolution, as a practically oriented algorithm, is widely used in state-of-art modern…
We compare the model-theoretic expressiveness of the existential fragment of Separation Logic over unrestricted relational signatures (SLR) -- with only separating conjunction as logical connective and higher-order inductive definitions,…
We consider the extension of the two-variable guarded fragment logic with local Presburger quantifiers. These are quantifiers that can express properties such as "the number of incoming blue edges plus twice the number of outgoing red edges…
The treewidth boundedness problem for a logic asks for the existence of an upper bound on the treewidth of the models of a given formula in that logic. This problem is found to be undecidable for first order logic. We consider a…
Separation Logic with inductive definitions is a well-known approach for deductive verification of programs that manipulate dynamic data structures. Deciding verification conditions in this context is usually based on user-provided lemmas…
Pointer arithmetic is widely used in low-level programs, e.g. memory allocators. The specification of such programs usually requires using pointer arithmetic inside inductive definitions to define the common data structures, e.g. heap lists…
The logic of bunched implication BI provides a framework for reasoning about resource composition and forms the basis for an assertion language of separation logic which is used to reason about software programs. Propositional BI is…
Subexponential logic is a variant of linear logic with a family of exponential connectives--called subexponentials--that are indexed and arranged in a pre-order. Each subexponential has or lacks associated structural properties of weakening…
We study the guarded negation fragment of transitive closure logic (GNTC). We show that the satisfiability problem for GNTC is 2ExpTime-complete, by establishing the following reductions: (i) a polynomial-time reduction from the…
In previous works, a tableau calculus has been defined, which constitutes a decision procedure for hybrid logic with the converse and global modalities and a restricted use of the binder. This work shows how to extend such a calculus to…
The finite satisfiability problem for guarded fixpoint logic is decidable and complete for 2ExpTime (resp. ExpTime for formulas of bounded width).
Separation Logic (SL) is a well-known assertion language used in Hoare-style modular proof systems for programs with dynamically allocated data structures. In this paper we investigate the fragment of first-order SL restricted to the…
Separation logic is a concise method for specifying programs that manipulate dynamically allocated storage. Partially inspired by separation logic, Implicit Dynamic Frames has recently been proposed, aiming at first-order tool support. In…
This paper gives a decision procedure for the validity of en- tailment of symbolic heaps in separation logic with Presburger arithmetic and arrays. The correctness of the decision procedure is proved under the condition that sizes of arrays…
In this paper we investigate the complexity of abduction, a fundamental and important form of non-monotonic reasoning. Given a knowledge base explaining the world's behavior it aims at finding an explanation for some observed manifestation.…
This paper presents a complete decision procedure for the entire quantifier-free fragment of Separation Logic ($\seplog$) interpreted over heaplets with data elements ranging over a parametric multi-sorted (possibly infinite) domain. The…
We investigate (quantifier-free) spatial constraint languages with equality, contact and connectedness predicates as well as Boolean operations on regions, interpreted over low-dimensional Euclidean spaces. We show that the complexity of…
For fragments L of first-order logic (FO) with counting quantifiers, we consider the definability problem, which asks whether a given L-formula can be equivalently expressed by a formula in some fragment of L without counting, and the more…
In this paper we study a Separation Logic of Relations (SLR) and compare its expressiveness to (Monadic)Second Order Logic (M)SO. SLR is based on the well-known Symbolic Heap fragment of Separation Logic, whose formulae are composed of…
We present CLTLB(D), an extension of PLTLB (PLTL with both past and future operators) augmented with atomic formulae built over a constraint system D. Even for decidable constraint systems, satisfiability and Model Checking problem of such…