Related papers: A Simple Functional Presentation and an Inductive …
We recently described a formalism for reasoning with if-then rules that re expressed with different levels of firmness [18]. The formalism interprets these rules as extreme conditional probability statements, specifying orders of magnitude…
Despite decades of research, there are still a number of concepts commonly found in software programs that are considered challenging for verification: among others, such concepts include concurrency, and the compositional analysis of…
We propose a hybrid-dynamic first-order logic as a formal foundation for specifying and reasoning about reconfigurable systems. As the name suggests, the formalism we develop extends (many-sorted) first-order logic with features that are…
Formal, automated theorem proving has long been viewed as a challenge to artificial intelligence. We introduce here a new approach to computer theorem proving, one that employs specialized language models for Lean4 proof generation combined…
Many semantical aspects of programming languages, such as their operational semantics and their type assignment calculi, are specified by describing appropriate proof systems. Recent research has identified two proof-theoretic features that…
We take a formal approach to the explainability problem of machine learning systems. We argue against the practice of interpreting black-box models via attributing scores to input components due to inherently conflicting goals of…
A theory of recursive and corecursive definitions has been developed in higher-order logic (HOL) and mechanized using Isabelle. Least fixedpoints express inductive data types such as strict lists; greatest fixedpoints express coinductive…
Many Program Verification and Synthesis problems of interest can be modeled directly using Horn clauses and many recent advances in the CLP and CAV communities have centered around efficiently solving problems presented as Horn clauses. The…
The task of inferring logical formulas from examples has garnered significant attention as a means to assist engineers in creating formal specifications used in the design, synthesis, and verification of computing systems. Among various…
Conformal predictors are machine learning algorithms that output prediction sets that have a guarantee of marginal validity for finite samples with minimal distributional assumptions. This is a property that makes conformal predictors…
In is paper we present a labelled tableau proof system that serves a wide class of interpretability logics. The system is proved sound and complete for any interpretability logic characterised by a frame condition given by a set of…
A new, flexible inference method for Horn logic program is proposed, which is a drastic generalization of chart parsing, partial instantiations of clauses in a program roughly corresponding to arcs in a chart. Chart-like parsing and…
We propose an algorithm that test membership for regular expressions and show that the algorithm is correct. This algorithm is written in the style of a sequent proof system. The advantage of this algorithm over traditional ones is that the…
Let c>0 be a constant, and $\Phi$ be a random Horn formula with n variables and $m=c\cdot 2^{n}$ clauses, chosen uniformly at random (with repetition) from the set of all nonempty Horn clauses in the given variables. By analyzing \PUR, a…
Logic Programming is a Turing complete language. As a consequence, designing algorithms that decide termination and non-termination of programs or decide inductive/coinductive soundness of formulae is a challenging task. For example, the…
Recent years have witness remarkable performance improvements in maximum satisfiability (MaxSAT) solvers. In practice, MaxSAT algorithms often target the most generic MaxSAT formulation, whereas dedicated solvers, which address specific…
We show that verification of object-oriented programs by means of the assertional method can be achieved in a simple way by exploiting a syntax-directed transformation from object-oriented programs to recursive programs. This transformation…
This paper aims at carrying out termination proofs for simply typed higher-order calculi automatically by using ordering comparisons. To this end, we introduce the computability path ordering (CPO), a recursive relation on terms obtained by…
We show that a partial-correctness assertion about an iterative program is provable in Hoare Logic iffit is provable in standard second-order logic with comprehension restricted to first-order predicates. This equivalence was claimed twice…
We provide a sound and relatively complete Hoare-like proof system for reasoning about partial correctness of recursive procedures in presence of local variables and the call-by-value parameter mechanism, and in which the correctness proofs…