Related papers: Verifiers and Generators: Epistemic Semantics for …
We present realizability and realization logic, two program logics that jointly address the problem of finding solutions in semantics-guided synthesis. What is new is that we proceed eagerly and not only analyze a single candidate program…
Intuitionistic epistemic logic introduces an epistemic operator, which reflects the intended BHK semantics of intuitionism, to intuitionistic logic. The fundamental assumption concerning intuitionistic knowledge and belief is that it is the…
Epistemic logic programs constitute an extension of the stable models semantics to deal with new constructs called subjective literals. Informally speaking, a subjective literal allows checking whether some regular literal is true in all…
This is the author's Ph.D. Thesis. It contains results from four years of research into realizability and categorical logic. The main subjects are the axiomatisation of realizable propositions, and a characterization of realizability…
This article examines two approaches to verification, one based on using a logic for expressing properties of a system, and one based on showing the system equivalent to a simpler system that obviously has whatever property is of interest.…
We introduce the problem of temporal coverability for realizability and synthesis. Namely, given a language of words that must be covered by a produced system, how to automatically produce such a system. We consider the case of coverability…
This paper introduces a general framework for generate-and-test-based solvers for epistemic logic programs that can be instantiated with different generator and tester programs, and we prove sufficient conditions on those programs for the…
In generic realizability for set theories, realizers treat unbounded quantifiers generically. To this form of realizability, we add another layer of extensionality by requiring that realizers ought to act extensionally on realizers, giving…
We show that including degrees of a particular kind of provability in the search target for any theorem-prover in sufficiently powerful formal systems over finite-sized statements preserves well-definition and a sufficient consistency while…
This paper presents a formal theory of verification and validation (V&V) within systems engineering, grounded in the axiom that V&V are fundamentally knowledge-building activities. Using dynamic epistemic modal logic, we develop precise…
Despite significant developments in Proof Theory, surprisingly little attention has been devoted to the concept of proof verifier. In particular, the mathematical community may be interested in studying different types of proof verifiers…
We analyze the informal semantic conception of proof and axiomatize the proof relation and the provability operator. A self referential propositional calculus which admits provable liar type sentences is introduced and proven consistent. We…
Transformers have been shown to emulate logical deduction over natural language theories (logical rules expressed in natural language), reliably assigning true/false labels to candidate implications. However, their ability to generate…
We derive a Prolog theorem prover for an Intuitionistic Epistemic Logic by starting from the sequent calculus {\bf G4IP} that we extend with operator definitions providing an embedding in intuitionistic propositional logic ({\bf IPC}). With…
Recent research in extensions of Answer Set Programming has included a renewed interest in the language of Epistemic Specifications, which adds modal operators K ("known") and M ("may be true") to provide for more powerful introspective…
We give a relational and a weakest precondition semantics for "knowledge-based programs", i.e., programs that restrict observability of variables so as to richly express changes in the knowledge of agents who can or cannot observe said…
The language of epistemic specifications and epistemic logic programs extends disjunctive logic programs under the stable model semantics with modal constructs called subjective literals. Using subjective literals, it is possible to check…
We propose a fragment of many-sorted second order logic called EQSMT and show that checking satisfiability of sentences in this fragment is decidable. EQSMT formulae have an $\exists^*\forall^*$ quantifier prefix (over variables, functions…
Realizability for knowledge representation formalisms studies the following question: given a semantics and a set of interpretations, is there a knowledge base whose semantics coincides exactly with the given interpretation set? We…
Real-valued logics underlie an increasing number of neuro-symbolic approaches, though typically their logical inference capabilities are characterized only qualitatively. We provide foundations for establishing the correctness and power of…