Related papers: A Program Logic for Abstract (Hyper)Properties
We propose a purely extensional semantics for higher-order logic programming. In this semantics program predicates denote sets of ordered tuples, and two predicates are equal iff they are equal as sets. Moreover, every program has a unique…
Synthesizing programs from examples requires searching over a vast, combinatorial space of possible programs. In this search process, a key challenge is representing the behavior of a partially written program before it can be executed, to…
First-order linear temporal logic (FOLTL) is a flexible and expressive formalism capable of naturally describing complex behaviors and properties. Although the logic is in general highly undecidable, the idea of using it as a specification…
Category theory can be used to state formulas in First-Order Logic without using set membership. Several notable results in logic such as proof of the continuum hypothesis can be elegantly rewritten in category theory. We propose in this…
Applying Large Language Models (LLMs) to heterogeneous enterprise systems is hindered by hallucinations and failures in multi-hop, n-ary reasoning. Existing paradigms (e.g., GraphRAG, NL2SQL) lack the semantic grounding and auditable…
While Large Language Models (LLMs) demonstrate remarkable proficiency in semantic understanding, they often struggle to ensure structural consistency and reasoning reliability in complex decision-making tasks that demand rigorous logic.…
We present a generic framework that facilitates object level reasoning with logics that are encoded within the Higher Order Logic theorem proving environment of HOL Light. This involves proving statements in any logic using intuitive…
We introduce a proof language for Intuitionistic Multiplicative Additive Linear Logic (IMALL), extended with a modality B to capture mixed-state quantum computation. The language supports algebraic constructs such as linear combinations,…
Applying dynamic logics to program verifications is a challenge, because their axiomatic rules for regular expressions can be difficult to be adapted to different program models. We present a novel dynamic logic, called DLp, which supports…
Abstract semantics has proven to be instrumental for accelerating search-based program synthesis, by enabling the sound pruning of a set of incorrect programs (without enumerating them). One may expect faster synthesis with increasingly…
Inductive program synthesis, or inferring programs from examples of desired behavior, offers a general paradigm for building interpretable, robust, and generalizable machine learning systems. Effective program synthesis depends on two key…
The general completeness problem of Hoare logic relative to the standard model $N$ of Peano arithmetic has been studied by Cook, and it allows for the use of arbitrary arithmetical formulas as assertions. In practice, the assertions would…
Hoare-style program logics are a popular and effective technique for software verification. Relational program logics are an instance of this approach that enables reasoning about relationships between the execution of two or more programs.…
Often times, we specify tasks for a robot using temporal language that can also span different levels of abstraction. The example command ``go to the kitchen before going to the second floor'' contains spatial abstraction, given that…
Game comonads provide categorical semantics for comparison games in Finite Model Theory, thus providing an abstract characterisation of logical equivalence for a wide range of logics, each one captured through a specific choice of comonad.…
We propose a novel logic, called Frame Logic (FL), that extends first-order logic (with recursive definitions) using a construct Sp(.) that captures the implicit supports of formulas -- the precise subset of the universe upon which their…
The relationship between abstract interpretation and partial deduction has received considerable attention and (partial) integrations have been proposed starting from both the partial deduction and abstract interpretation perspectives. In…
Hoare logic provides a syntax-oriented method to reason about program correctness and has been proven effective in the verification of classical and probabilistic programs. Existing proposals for quantum Hoare logic either lack completeness…
A logic programming paradigm which expresses solutions to problems as stable models has recently been promoted as a declarative approach to solving various combinatorial and search problems, including planning problems. In this paradigm,…
The idea of using unfolding as a way of computing a program semantics has been applied successfully to logic programs and has shown itself a powerful tool that provides concrete, implementable results, as its outcome is actually source…