计算机科学中的逻辑
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…
Real-valued logics have seen a renewed interest in verification for probabilistic and quantitative systems, in particular machine learning models, where they can be used to directly integrate specifications in the training objective. To do…
We start a systematic investigation of the size of Craig interpolants, uniform interpolants, and strongest implicates for (quasi-)normal modal logics. Our main upper bound states that for tabular modal logics, the computation of strongest…
The so-called algebraic approach to the constraint satisfaction problem (CSP) has been a prevalent method of the study of complexity of these problems since early 2000's. The core of this approach is the notion of polymorphisms which…
Short-circuit evaluation denotes the semantics of propositional connectives in which the second argument is evaluated only if the first argument does not suffice to determine the value of the expression. Short-circuit evaluation is widely…
Proposition algebra is based on Hoare's conditional connective, which is a ternary connective comparable to if-then-else and used in the setting of propositional logic. Conditional statements are provided with a simple semantics that is…
There has recently been exciting progress in the realm of *probabilistic separation logics*. An important subclass of these -- including PSL, Lilac, Bluebell, and pcOL -- are *general-purpose probabilistic logics* (or GPLs, for short),…
Runtime verification enables checking temporal logic specifications over individual execution traces and offers a scalable alternative to exhaustive formal verification. In practice, systems must satisfy dozens to hundreds of temporal…
Description logics (DL) are a family of formal languages for representing and reasoning about structured knowledge in terms of concepts and their relationships. A central reasoning problem in DL is concept subsumption. Although this problem…
We present a categorical theory of monads and distributive laws in substructural contexts. In the study of distributive laws, the roles of (the absence of) structural rules for variable contexts have been recognized; our theory formalizes…
The literature on ontology-mediated query answering (OMQA) has been shaped by two key results: first-order rewritability for DL-Lite, and PTime-hardness of data complexity for essentially every description logic beyond it. This has…
We present a formalization of the technical language of Navya-Nyaya - the "New Logic" school of late-classical Indian philosophy - in CCHM De Morgan cubical type theory (CTT). Previous formalization attempts in first-order logic (Matilal),…
Biprofile deviation logic models strategic social choice states as pairs $(R,P)$, where $R$ is the true profile used for welfare comparisons and $P$ is the submitted report profile used by the rule. Coalition modalities replace only the…
We introduce ProofGrid, a benchmark suite for evaluating LLM reasoning through machine-checkable proofs rather than final answers alone. ProofGrid contains 15 tasks spanning proof writing, proof checking, proof masking, and proof…
Computing optimal conditional reachability probabilities in Markov decision processes (MDPs) is tractable by a reduction to reachability probabilities. Yet, this reduction yields cyclic, challenging MDPs that are often notoriously hard to…
Shielding is a prominent model-based technique to ensure safety of autonomous agents. Classical shielding aims to ensure that nothing bad ever happens and comes with strong guarantees about safety and maximal permissiveness. However,…
The ecosystem of Lean and Mathlib has become the de facto standard for large language model (LLM) assisted formal reasoning with remarkable successes in recent years. Those successes, however, only consume Mathlib as an essential dependency…
Recently, symbolic structures were proposed as finite representations of potentially infinite first-order structures, where Linear Integer Arithmetic terms and formulas define the domain and interpretations of a structure. We generalize…
Fixed points are a recurring theme in computer science and are often constructed as limits of suitably seeded fixed point iterations. We present the algebra of iterative constructions (AIC) -- a purely algebraic approach to reasoning about…
As schema languages for RDF data become more mature, we are seeing efforts to extend them with recursive semantics, applying diverse ideas from logic programming and description logics. While ShEx has an official recursive semantics based…