Related papers: Proof Compression via Subatomic Logic and Guarded …
Lipton's reduction theory provides an intuitive and simple way for deducing the non-interference properties of concurrent programs, but it is difficult to directly apply the technique to verify linearizability of sophisticated fine-grained…
LLM-powered agents often use prompt compression to reduce inference costs, but this introduces a new security risk. Compression modules, which are optimized for efficiency rather than safety, can be manipulated by adversarial inputs,…
A grammar logic refers to an extension to the multi-modal logic K in which the modal axioms are generated from a formal grammar. We consider a proof theory, in nested sequent calculus, of grammar logics with converse, i.e., every modal…
Data-driven artificial intelligence (AI) techniques are becoming prominent for learning in support of data compression, but are focused on standard problems such as text compression. To instead address the emerging problem of semantic…
Partial incorrectness logic (partial reverse Hoare logic) has recently been introduced as a new Hoare-style logic that over-approximates the weakest pre-conditions of a program and a post-condition. It is expected to verify systems where…
We try to bring to light some combinatorial structure underlying formal proofs in logic. We do this through the study of the Craig Interpolation Theorem which is properly a statement about the structure of formal derivations. We show that…
We introduce propositional team-based logics expressively complete for (quasi) downward and (quasi) upward closed properties in a syntactically dual way, by using variants of the inclusion atom. In particular, the variants of the primitive…
Over the past two decades several fragments of first-order logic have been identified and shown to have good computational and algorithmic properties, to a great extent as a result of appropriately describing the image of the standard…
It is well-known that extending the Hilbert axiomatic system for first-order intuitionistic logic with an exclusion operator, that is dual to implication, collapses the domains of models into a constant domain. This makes it an interesting…
Nominal Logic is a version of first-order logic with equality, name-binding, renaming via name-swapping and freshness of names. Contrarily to higher-order logic, bindable names, called atoms, and instantiable variables are considered as…
Prolog's very useful expressive power is not captured by traditional logic programming semantics, due mainly to the cut and goal and clause order. Several alternative semantics have been put forward, exposing operational details of the…
We extend the simply-typed guarded $\lambda$-calculus with discrete probabilities and endow it with a program logic for reasoning about relational properties of guarded probabilistic computations. This provides a framework for programming…
We present a logic named L_{LF} whose intended use is to formalize properties of specifications developed in the dependently typed lambda calculus LF. The logic is parameterized by the LF signature that constitutes the specification. Atomic…
Contextual refinement and separation logics are successful verification techniques that are very different in nature. First, the former guarantees behavioral refinement between a concrete program and an abstract program while the latter…
According to a theorem of Courcelle monadic second-order logic and guarded second-order logic (where one can also quantify over sets of edges) have the same expressive power over the class of all countable $k$-sparse hypergraphs. In the…
We give a new characterization of elementary and deterministic polynomial time computation in linear logic through the proofs-as-programs correspondence. Girard's seminal results, concerning elementary and light linear logic, achieve this…
We study atom canonicity for several varieties of cylindric like algebras that contain properly the variety of representable algebras. The algebras in such varieties have relativized representations, and we thereby obtain many omitting…
Cumulative logics are studied in an abstract setting, i.e., without connectives, very much in the spirit of Makinson's early work. A powerful representation theorem characterizes those logics by choice functions that satisfy a weakening of…
We explore the consequences of layering a Lambek proof system over an arbitrary (constraint) logic. A simple model-theoretic semantics for our hybrid language is provided for which a particularly simple combination of Lambek's and the proof…
When a system commits to a hypothesis, much of the evidential structure behind that commitment is lost to compression. Standard accounts assume that selected content and scalar confidence suffice for downstream control. This paper argues…