Related papers: Proof systems for partial incorrectness logic (par…
The paper presents probabilistic extensions of interval temporal logic (ITL) and duration calculus (DC) with infinite intervals and complete Hilbert-style proof systems for them. The completeness results are a strong completeness theorem…
We present a new system S for handling uncertainty in a quantified modal logic (first-order modal logic). The system is based on both probability theory and proof theory. The system is derived from Chisholm's epistemology. We concretize…
Distributed systems are critical to reliable and scalable computing; however, they are complicated in nature and prone to bugs. To modularly manage this complexity, network middleware has been traditionally built in layered stacks of…
The provability logic of a theory $T$ captures the structural behavior of formalized provability in $T$ as provable in $T$ itself. Like provability, one can formalize the notion of relative interpretability giving rise to interpretability…
A coverage type generalizes refinement types found in many functional languages with support for must-style underapproximate reasoning. Property-based testing frameworks are one particularly useful domain where such capabilities are useful…
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…
Logical paradoxes and inconsistent information pose deep challenges in epistemology and the philosophy of logic. Classical systems typically handle contradictions only through external checks or by altering the logical framework, as in…
We will investigate proof-theoretic and linguistic aspects of first-order linear logic. We will show that adding partial order constraints in such a way that each sequent defines a unique linear order on the antecedent formulas of a sequent…
Local Completeness Logic (LCL) has been put forward as a program logic for proving both the correctness and incorrectness of program specifications. LCL is an abstract logic, parameterized by an abstract domain that allows combining over-…
We develop a formal theory of the weak values with emphasis on the consistency conditions and a probabilistic interpretation in the counter-factual processes. We present the condition for the choice of the post-selected state to give a…
In the same sense as classical logic is a formal theory of truth, the recently initiated approach called computability logic is a formal theory of computability. It understands (interactive) computational problems as games played by a…
This paper presents a Hoare-style calculus for formal reasoning about reconfiguration programs of distributed systems. Such programs create and delete components and/or interactions (connectors) while the system components change state…
In this paper we formulate the problem of inference under incomplete information in very general terms. This includes modelling the process responsible for the incompleteness, which we call the incompleteness process. We allow the process…
We aim at a holistic perspective on program logics, including Hoare and incorrectness logics. To this end, we study different classes of properties arising from the generalization of the aforementioned logics. We compare our results with…
The paper presents partial-realization theory and realization algorithms for linear switched systems. Linear switched systems are a particular subclass of hybrid systems. We formulate a notion of a partial realization and we present…
Separation logics are a family of extensions of Hoare logic for reasoning about programs that mutate memory. These logics are "abstract" because they are independent of any particular concrete memory model. Their assertion languages, called…
Many optimization problems of interest are known to be intractable, and while there are often heuristics that are known to work on typical instances, it is usually not easy to determine a posteriori whether the optimal solution was found.…
While there is a long tradition of reasoning about (non)termination in program analysis, specialized logics are typically needed to give different termination criteria. This includes partial correctness, where termination is not guaranteed,…
Reliable verification of proofs remains a bottleneck for training and evaluating AI systems on hard mathematical reasoning. Fully formal proofs, in languages like Lean, are easy to verify because they are unambiguous and modular. Most…
A weak form of the Circle Criterion for Lur'e systems is stated. The result allows prove global boundedness of all system solutions. Moreover such a result can be employed to enlarge the set of nonlinearities for which the standard Circle…