Related papers: Formally Verified SAT-Based AI Planning
The proof of the relative consistency of the axiom of choice has been mechanized using Isabelle/ZF. The proof builds upon a previous mechanization of the reflection theorem. The heavy reliance on metatheory in the original proof makes the…
Fully observable non-deterministic (FOND) planning is becoming increasingly important as an approach for computing proper policies in probabilistic planning, extended temporal plans in LTL planning, and general plans in generalized…
Isabelle is a generic theorem prover with a fragment of higher-order logic as a metalogic for defining object logics. Isabelle also provides proof terms. We formalize this metalogic and the language of proof terms in Isabelle/HOL, define an…
Despite the vast body of research literature proposing algorithms with formal guarantees, the amount of verifiable code in today's systems remains minimal. This discrepancy stems from the inherent difficulty of verifying code, particularly…
All solutions SAT (AllSAT for short) is a variant of propositional satisfiability problem. Despite its significance, AllSAT has been relatively unexplored compared to other variants. We thus survey and discuss major techniques of AllSAT…
We present a novel propositional proof tracing format that eliminates complex processing, thus enabling efficient (formal) proof checking. The benefits of this format are demonstrated by implementing a proof checker in C, which outperforms…
Logic Artificial Intelligence (AI) is a subfield of AI where variables can take two defined arguments, True or False, and are arranged in clauses that follow the rules of formal logic. Several problems that span from physical systems to…
We present a method for verifying the correctness of imperative programs which is based on the automated transformation of their specifications. Given a program prog, we consider a partial correctness specification of the form $\{\varphi\}$…
In this article we demonstrate how to solve a variety of problems and puzzles using the built-in SAT solver of the computer algebra system Maple. Once the problems have been encoded into Boolean logic, solutions can be found (or shown to…
We introduce lower-bound certificates for classical planning tasks, which can be used to prove the unsolvability of a task or the optimality of a plan in a way that can be verified by an independent third party. We describe a general…
There is a long tradition of fruitful interaction between logic and social choice theory. In recent years, much of this interaction has focused on computer-aided methods such as SAT solving and interactive theorem proving. In this paper, we…
And-Inverter Graphs (AIGs) are a popular way to represent Boolean functions (like circuits). AIG simplification algorithms can dramatically reduce an AIG, and play an important role in modern hardware verification tools like equivalence…
Mechanized theorem proving is becoming the basis of reliable systems programming and rigorous mathematics. Despite decades of progress in proof automation, writing mechanized proofs still requires engineers' expertise and remains labor…
In this paper we focus on the development of a toolbox for the verification of programs in the context of SCOOP -- an elegant concurrency model, recently formalized based on Rewriting Logic (RL) and Maude. SCOOP is implemented in Eiffel and…
We propose bounded fitting as a scheme for learning description logic concepts in the presence of ontologies. A main advantage is that the resulting learning algorithms come with theoretical guarantees regarding their generalization to…
We show that verification of object-oriented programs by means of the assertional method can be achieved in a simple way by exploiting a syntax-directed transformation from object-oriented programs to recursive programs. This transformation…
Writing accurate numerical software is hard because of many sources of unavoidable uncertainties, including finite numerical precision of implementations. We present a programming model where the user writes a program in a real-valued…
SMT-based program analysis and verification often involve reasoning about program features that have been specified using quantifiers; incorporating quantifiers into SMT-based reasoning is, however, known to be challenging. If quantifier…
In various scenarios, a single phase of modelling and solving is either not sufficient or not feasible to solve the problem at hand. A standard approach to solving AI planning problems, for example, is to incrementally extend the planning…
The amount of information in satisfiability problem (SAT) is considered. SAT can be polynomial-time solvable when the solving algorithm holds an exponential amount of information. It is also established that SAT Kolmogorov complexity is…