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We introduce heap automata, a formalism for automatic reasoning about robustness properties of the symbolic heap fragment of separation logic with user-defined inductive predicates. Robustness properties, such as satisfiability,…
Judgmental forecasting employs human opinions to make predictions about future events, rather than exclusively historical data as in quantitative forecasting. When these opinions form an argumentative structure around forecasts, it is…
Craig interpolation is a fundamental property of classical and non-classic logics with a plethora of applications from philosophical logic to computer-aided verification. The question of which interpolants can be obtained from an…
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…
Higher-order functions and imperative states are language features supported by many mainstream languages. Their combination is expressive and useful, but complicates specification and reasoning, due to the use of yet-to-be-instantiated…
Hybrid logic extends modal logic with support for reasoning about individual states, designated by so-called nominals. We study hybrid logic in the broad context of coalgebraic semantics, where Kripke frames are replaced with coalgebras for…
Axioms are presented which encapsulate the properties satisfied by categories of games which form the basis of results on full abstraction for PCF and other programming languages, and on full completeness for various logics and type…
Before deploying outputs from foundation models in high-stakes tasks, it is imperative to ensure that they align with human values. For instance, in radiology report generation, reports generated by a vision-language model must align with…
This paper presents a language-independent proof system for reachability properties of programs written in non-deterministic (e.g., concurrent) languages, referred to as all-path reachability logic. It derives partial-correctness properties…
Reasoning-capable LLMs have achieved major breakthroughs in solving complex problems, but recent work shows that acquiring and deploying strong reasoning can introduce significant safety risks. A common mitigation is to apply a secondary…
Modern functional-logic programming languages like Toy or Curry feature non-strict non-deterministic functions that behave under call-time choice semantics. A standard formulation for this semantics is the CRWL logic, that specifies a proof…
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…
We give a calculus for reasoning about the first-order fragment of classical logic that is adequate for giving the truth conditions of intuitionistic Kripke frames, and outline a proof-theoretic soundness and completeness proof, which we…
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…
Program logics for bug-finding (such as the recently introduced Incorrectness Logic) have framed correctness and incorrectness as dual concepts requiring different logical foundations. In this paper, we argue that a single unified theory…
We investigate a recently-devised polyhedral semantics for intermediate logics, in which formulas are interpreted in n-dimensional polyhedra. An intermediate logic is polyhedrally complete if it is complete with respect to some class of…
DHOL is an extensional, classical logic that equips the well-known higher-order logic (HOL) with dependent types. This allows for concise encodings of important domains like size-bounded data structures, category theory, or proof theory.…
Constraint Handling Rules (CHR) is a rule-based programming language which is typically embedded into a general-purpose language. There exists a plethora of implementations for numerous host languages. However, the existing implementations…
The automated proof search system and decidability for logic of correlated knowledge is presented in this paper. The core of the proof system is the sequent calculus with the properties of soundness, completeness, admissibility of cut and…
Foundational verification considers the functional correctness of programming languages with formalized semantics and uses proof assistants (e.g., Coq, Isabelle) to certify proofs. The need for verifying complex programs compels it to…