We analyze the notions of independence of a set of postulates, proposed by G. Peano, E. H. Moore, A. Church and F. Harary, together with a presumably new notion inspired by H. M. Sheffer. For each of these notions, we present a proper definition and give illustrative examples. We give a complete picture of the implications between these notions of independence. Then, we make some additional observations that shed some light on these notions and some concepts related to them.
我们分析了由G. Peano, E. H. Moore, a . Church和F. Harary提出的一组公设的独立性概念，以及由H. M. Sheffer启发的一个可能的新概念。对于每一个概念，我们都给出了适当的定义，并给出了说明性的例子。我们给出了这些独立概念之间含义的完整图景。然后，我们做一些额外的观察来阐明这些概念和与之相关的一些概念。
{"title":"Notions of Independence: Examples and Properties","authors":"Bruno Bandeira, Márcia R. Cerioli, Petrucio Viana","doi":"10.5753/WBL.2021.15775","DOIUrl":"https://doi.org/10.5753/WBL.2021.15775","url":null,"abstract":"We analyze the notions of independence of a set of postulates, proposed by G. Peano, E. H. Moore, A. Church and F. Harary, together with a presumably new notion inspired by H. M. Sheffer. For each of these notions, we present a proper definition and give illustrative examples. We give a complete picture of the implications between these notions of independence. Then, we make some additional observations that shed some light on these notions and some concepts related to them.","PeriodicalId":231385,"journal":{"name":"Anais do II Workshop Brasileiro de Lógica (WBL 2021)","volume":"8 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120927330","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In critical systems, failures or errors can cause catastrophes, such as deaths or considerably losses of money. Model checking provides an automated way to prove the correctness of programs' requirements. It is a convenient technique to use in systems that need reliability. Propositional Dynamic Logic (PDL) is a formal system designed to reason about programs. This work presents a compiler implementation from a subset of the C language and also for the Smacco model, both to the PDL language, and after that to the language of the nuXmv model checker. This implementation is linked with a Blockchain model generation system to model and reason about smart contracts.
{"title":"Automatic program verification in Dynamic Logic with applications to smart contracts","authors":"A. Patrick, I. M. Coelho, Bruno Lopes","doi":"10.5753/WBL.2021.15772","DOIUrl":"https://doi.org/10.5753/WBL.2021.15772","url":null,"abstract":"In critical systems, failures or errors can cause catastrophes, such as deaths or considerably losses of money. Model checking provides an automated way to prove the correctness of programs' requirements. It is a convenient technique to use in systems that need reliability. Propositional Dynamic Logic (PDL) is a formal system designed to reason about programs. This work presents a compiler implementation from a subset of the C language and also for the Smacco model, both to the PDL language, and after that to the language of the nuXmv model checker. This implementation is linked with a Blockchain model generation system to model and reason about smart contracts.","PeriodicalId":231385,"journal":{"name":"Anais do II Workshop Brasileiro de Lógica (WBL 2021)","volume":"125 17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127793049","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. F. Ramos, Ruy J. G. B. de Queiroz, Anjolina Grisi de Oliveira
A relação de conversão entre termos dada por Church, que determina a igualdade entre termos, diz que dois λ-termos são o mesmo se forem conversíveis um ao outro. Em outras palavras, um caminho entre dois termos, o que sugere a possibilidade de uma semântica com base em homotopia.
{"title":"Conversão de Termos, Homotopia, e Estrutura de Grupóide","authors":"A. F. Ramos, Ruy J. G. B. de Queiroz, Anjolina Grisi de Oliveira","doi":"10.5753/WBL.2021.15776","DOIUrl":"https://doi.org/10.5753/WBL.2021.15776","url":null,"abstract":"A relação de conversão entre termos dada por Church, que determina a igualdade entre termos, diz que dois λ-termos são o mesmo se forem conversíveis um ao outro. Em outras palavras, um caminho entre dois termos, o que sugere a possibilidade de uma semântica com base em homotopia.","PeriodicalId":231385,"journal":{"name":"Anais do II Workshop Brasileiro de Lógica (WBL 2021)","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114713445","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Este é um trabalho em andamento sobre a resolução de equações e diferenças entre termos nominais, chamado de problema de desunificação nominal. Ao invés de usarmos as técnicas nominais padrões que envolvem restrições de freshness (i.e., expressões da forma a#t que significa "o átomo a não ocorre livre em t'') para implementar alpha-equivalência, seguiremos uma abordagem alternativa que envolve equações de ponto fixo, i.e., equações da forma pi.t=_alpha t, onde t é um termo nominal e pi uma permutação. Essa abordagem será conveniente a futuras extensões do problema envolvendo teorias equacionais.
{"title":"Desunificação Nominal via Ponto Fixo","authors":"L. Batista, Daniele Nantes-Sobrinho","doi":"10.5753/WBL.2021.15773","DOIUrl":"https://doi.org/10.5753/WBL.2021.15773","url":null,"abstract":"Este é um trabalho em andamento sobre a resolução de equações e diferenças entre termos nominais, chamado de problema de desunificação nominal. Ao invés de usarmos as técnicas nominais padrões que envolvem restrições de freshness (i.e., expressões da forma a#t que significa \"o átomo a não ocorre livre em t'') para implementar alpha-equivalência, seguiremos uma abordagem alternativa que envolve equações de ponto fixo, i.e., equações da forma pi.t=_alpha t, onde t é um termo nominal e pi uma permutação. Essa abordagem será conveniente a futuras extensões do problema envolvendo teorias equacionais.","PeriodicalId":231385,"journal":{"name":"Anais do II Workshop Brasileiro de Lógica (WBL 2021)","volume":"461 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123099764","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper presents the (second-order) theory of hereditarily finite sets according to the usual pattern adopted in the presentation of the (second-order) theory of natural numbers. To this purpose, we consider three primitive concepts, together with four axioms, which are analogous to the usual Peano axioms. From them, we prove a homomorphism theorem, its converse, categoricity, and a kind of (semantical) completeness.
{"title":"An Arithmetical-like Theory of Hereditarily Finite Sets","authors":"Márcia R. Cerioli, Vitor Krauss, Petrucio Viana","doi":"10.5753/WBL.2021.15774","DOIUrl":"https://doi.org/10.5753/WBL.2021.15774","url":null,"abstract":"This paper presents the (second-order) theory of hereditarily finite sets according to the usual pattern adopted in the presentation of the (second-order) theory of natural numbers. To this purpose, we consider three primitive concepts, together with four axioms, which are analogous to the usual Peano axioms. From them, we prove a homomorphism theorem, its converse, categoricity, and a kind of (semantical) completeness.","PeriodicalId":231385,"journal":{"name":"Anais do II Workshop Brasileiro de Lógica (WBL 2021)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122739225","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This work introduces the variety of perfect paradefinite algebras (PPalgebras), consisting of De Morgan algebras enriched with a perfect operator o, which turns out to be equivalent to the variety of involutive Stone algebras (IS-algebras). The corresponding order-preserving logic PP≤ is a Logic of Formal Inconsistency, a Logic of Formal Undeterminedness, a C-system and a D-system, some of these features being evident in the proposed axiomatization of PP-algebras. After proving the mentioned algebraic equivalence, we show how to axiomatize, by means of Hilbert-style calculi, certain extensions of De Morgan algebras with a perfect operator and, in particular, the logic PP≤.
{"title":"Notes on the Logic of Perfect Paradefinite Algebras","authors":"Joel Felipe Ferreira Gomes, V. Greati","doi":"10.5753/WBL.2021.15777","DOIUrl":"https://doi.org/10.5753/WBL.2021.15777","url":null,"abstract":"This work introduces the variety of perfect paradefinite algebras (PPalgebras), consisting of De Morgan algebras enriched with a perfect operator o, which turns out to be equivalent to the variety of involutive Stone algebras (IS-algebras). The corresponding order-preserving logic PP≤ is a Logic of Formal Inconsistency, a Logic of Formal Undeterminedness, a C-system and a D-system, some of these features being evident in the proposed axiomatization of PP-algebras. After proving the mentioned algebraic equivalence, we show how to axiomatize, by means of Hilbert-style calculi, certain extensions of De Morgan algebras with a perfect operator and, in particular, the logic PP≤.","PeriodicalId":231385,"journal":{"name":"Anais do II Workshop Brasileiro de Lógica (WBL 2021)","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121788984","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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