Completeness for a First-order Abstract Separation Logic

Existing work on theorem proving for the assertion language of separation logic (SL) either focuses on abstract semantics which are not readily available in most applications of program verification, or on concrete models for which completeness is not possible. An important element in concrete SL is the points-to predicate which denotes a singleton heap. SL with the points-to predicate has been shown to be non-recursively enumerable. In this paper, we develop a first-order SL, called FOASL, with an abstracted version of the points-to predicate. We prove that FOASL is sound and complete with respect to an abstract semantics, of which the standard SL semantics is an instance. We also show that some reasoning principles involving the points-to predicate can be approximated as FOASL theories, thus allowing our logic to be used for reasoning about concrete program verification problems. We give some example theories that are sound with respect to different variants of separation logics from the literature, including those that are incompatible with Reynolds's semantics. In the experiment we demonstrate our FOASL based theorem prover which is able to handle a large fragment of separation logic with heap semantics as well as non-standard semantics.Comment: This is an extended version of the APLAS 2016 paper with the same titl

Bounding Resource Consumption with Gödel-Dummett Logics

International audienceGödel-Dummett logic LC and its finite approximations LCn are the intermediate logics complete w.r.t. linearly ordered Kripke models. In this paper, we use LCn logics as a tool to bound resource consumption in some process calculi. We introduce a non-deterministic process calculus where the consumption of a particular resource denoted * is explicit and provide an operational semantics which measures the consumption of this resource.We present a linear transformation of a process P into a formula f of LC. We show that the consumption of the resource by P can be bounded by the positive integer n if and only if the formula f admits a counter-model in LCn. Combining this result with our previous results on proof and counter-model construction for LCn, we conclude that bounding resource consumption is (linearly) equivalent to searching counter-models in LCn

LAPORAN MAGANG PROSES PRODUKSI, PENGENDALIAN MUTU DAN SANITASI DI PERUSAHAAN JAMU SABDO PALON DESA GATAK REJO KECAMATAN NGUTER KABUPATEN SUKOHARJO

Every company is expected to yields product that is with quality and safe consumed by public. For the purpose is required production process start from raw material handling up to handling of end product so that can yield product matching with SNI standard. Activity of this apprentice applied to add student knowledge in industrial world in general and to know more detailed about quality control in PJ. Sabdo Palon, Nguter, Sukoharjo. Activity of this apprentice executed on 3 Mey - 29 Mey 2010 di PJ. Sabdo Palon, Nguter, Sukoharjo. Data collecting method in this apprentice was executed with interview, observation, book study and downwards direct to field to do observation and joins in activity taking place in factory. Jamu is a product of natural ingredients from Indonesia, which is used for health maintenance, disease prevention, disease treatment, health recovery, fitness, and beauty. Jamu processing in factory can be divided into two, Jamu powders and Jamu pill. In PJ. Sabdo Palon, Nguter, Sukoharjo, Jamu powder processing begins with the compounding process and then followed a brief drying, milling, sieving, mixing, and packaging. For Jamu pill, after the Jamu powder finished, continued with mixing process and then compaction, pills molding, sorting pills, coating I, ovenizing, coating II and packaging. Quality control applied in the PJ. Sabdo Palon, starting from raw material acceptance until finished material packaging. Supervision of sanitation in the PJ. Palon Sabdo include materials sanitation, space and equipment sanitation, workers sanitation and waste handling. Production process waste include solid waste, wastewater, and other contaminated waste (eg dust). Kata Kunci : Production Processing, Jam

Towards a Proof Theory of G\"odel Modal Logics

Analytic proof calculi are introduced for box and diamond fragments of basic modal fuzzy logics that combine the Kripke semantics of modal logic K with the many-valued semantics of G\"odel logic. The calculi are used to establish completeness and complexity results for these fragments

Formulae-as-Resources Management for an Intuitionistic Theorem Prover

This paper outlines new concepts for an alternative implementation of the intuitionistic contraction-free LJT system (and consequently proof search) in imperative programming languages with a good and efficient management of formulae (as resources). Logic programming languages provide natural support to implement automated proof search, without necessity to have explicit knowledge about the form and the number of formulae arising in LJT proofs. By the introduction of a new notion of subformula (and of subformula property) for the LJT system, we obtain interesting and usable results about the possible management of formulae in a proof. A derived structure (a direct acyclic graph), including sharing of subformulae, is proposed to deal with formulae during the proof search and the application of logical rules. The corresponding proof search method is independent of the possible strategies. Therefore we can obtain an eOEcient implementation of LJT in imperative programming language..

Quantales as completions of ordered monoids: Revised semantics for Intuitionistic Linear Logic

The aim of this paper is to propose a unified analysis of the relationships between the notions of order and closure and to relate it to different semantics of Intuitionistic Linear Logic (ILL). We study the embedding of ordered monoids into quantales and then we propose general constructions and results about such an embedding. Therefore we obtain a new semantics based on ordered monoids and also new completeness results for ILL

Looking at Separation Algebras with Boolean BI-eyes

Part 2: Track B: Logic, Semantics, Specification and VerificationInternational audienceIn this paper, we show that the formulæ of Boolean BI cannot distinguish between some of the different notions of separation algebra found in the literature: partial commutative monoids, either cancellative or not, with a single unit or not, all define the same notion of validity. We obtain this result by the careful study of the specific properties of the counter-models that are generated by tableaux proof-search in Boolean B

Resource models and proof-search in Intuitionistic Linear Logic

Rapport interne.In this paper, we propose to investigate and to revise the semantics of Intuitionistic Linear Logic (\ILL), from an unified analysis of known semantics like phase semantics or Petri nets semantics. Thus, we focus on notions like quantale, closure and resource frames and we define a new semantics of \ILL\ that is called resource semantics. The completeness and the finite model property are proved from a based-on proof-search method in which countermodels are obtained from refutation trees. Moreover, we define a new preordered monoid semantics from an adequate choice of pretopology. As Petri nets can be seen as concrete representations of preordered monoids, such a choice also leads to a new Petri nets semantics for \ILL\ with new results like completeness and finite model property. From these semantical considerations, we obtain some results about non-provability in \ILL\ and then we can expect to develop methods for the generation of countermodels

Provability in Intuitionistic Linear Logic from a New Interpretation on Petri nets (Extended Abstract)

Linear logic is a logic of actions which seems well suited to various computer science applications. From its intrinsic ability to reflect computational resources, it is possible to refine different programming paradigms like formulae-as-types (proofsas -programs) or formulae-as-states (proofs-as-computations) with a finer control on resource management. In the latter case, the correspondence between Intuitionistic Linear Logic (ILL) and Petri nets illustrates the interest of efficient proof search methods for proving specifications or properties of distributed systems. In contrast to existing methods, for instance based on canonical proofs, we propose here to revisit the semantics of ILL and its interpretation on Petri nets to provide new proof techniques for proving or disproving properties. From the relationships between the notions of ordered monoid and of quantale we define a new interpretation of ILL on Petri nets that is complete and verifies the property of finite models. Possi..