Related papers: Encoding Peano Arithmetic in a Minimal Fragment of…
Hypothesis tests calibrated by (re)sampling methods (such as permutation, rank and bootstrap tests) are useful tools for statistical analysis, at the computational cost of requiring Monte-Carlo sampling for calibration. It is common and…
Two results are presented concerning the entailment problem in Separation Logic with inductively defined predicate symbols and theory reasoning. First, we show that the entailment problem is undecidable for rules with bounded tree-width, if…
An efficient entailment proof system is essential to compositional verification using separation logic. Unfortunately, existing decision procedures are either inexpressive or inefficient. For example, Smallfoot is an efficient procedure but…
Given a sequence $\{\Pi_n\}$ of Horn logic programs, the limit $\Pi$ of $\{\Pi_n\}$ is the set of the clauses such that every clause in $\Pi$ belongs to almost every $\Pi_n$ and every clause in infinitely many $\Pi_n$'s belongs to $\Pi$…
Most automated program verifiers for separation logic use either symbolic execution or verification condition generation to extract proof obligations, which are then handed over to an SMT solver. Existing verification algorithms are…
Quantitative separation logic (QSL) is an extension of separation logic (SL) for the verification of probabilistic pointer programs. In QSL, formulae evaluate to real numbers instead of truth values, e.g., the probability of memory-safe…
This paper presents matching logic, a first-order logic (FOL) variant for specifying and reasoning about structure by means of patterns and pattern matching. Its sentences, the patterns, are constructed using variables, symbols, connectives…
The aim of this work is to show that contemporary mathematics, including Peano arithmetic, is inconsistent, to construct firm foundations for mathematics, and to begin building on these foundations.
Warded Datalog+- extends the logic-based language Datalog with existential quantifiers in rule heads. Existential rules are needed for advanced reasoning tasks, e.g., ontological reasoning. The theoretical efficiency guarantees of Warded…
Verification of fault-tolerant distributed protocols is an immensely difficult task. Often, in these protocols, thresholds on set cardinalities are used both in the process code and in its correctness proof, e.g., a process can perform an…
In this article, we consider a simple representation for real numbers and propose top-down procedures to approximate various algebraic and transcendental operations with arbitrary precision. Detailed algorithms and proofs are provided to…
We specify the operational semantics and bisimulation relations for the finite pi-calculus within a logic that contains the nabla quantifier for encoding generic judgments and definitions for encoding fixed points. Since we restrict to the…
Locks are a classic data structure for concurrent programming. We introduce a type system to ensure that names of the asynchronous pi-calculus are used as locks. Our calculus also features a construct to deallocate a lock once we know that…
We present Lilac, a separation logic for reasoning about probabilistic programs where separating conjunction captures probabilistic independence. Inspired by an analogy with mutable state where sampling corresponds to dynamic allocation, we…
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…
High confidence in floating-point programs requires proving numerical properties of final and intermediate values. One may need to guarantee that a value stays within some range, or that the error relative to some ideal value is well…
We present a formal system for proving the partial correctness of a single-pass instruction sequence as considered in program algebra by decomposition into proofs of the partial correctness of segments of the single-pass instruction…
Several algorithms in computer algebra involve the computation of a power series solution of a given ordinary differential equation. Over finite fields, the problem is often lifted in an approximate $p$-adic setting to be well-posed. This…
Answer Set Programming (ASP) is an important logic programming paradigm within the field of Knowledge Representation and Reasoning. As a concise, human-readable, declarative language, ASP is an excellent tool for developing trustworthy…
Epistemic logic programs constitute an extension of the stable models semantics to deal with new constructs called subjective literals. Informally speaking, a subjective literal allows checking whether some regular literal is true in all…