An Unexpected Boolean Connective

Marcelino, Sérgio

doi:10.1007/s11787-021-00280-7

Cited by 5 publications

(3 citation statements)

References 28 publications

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“…All rules above serve both the single-and multiple-conclusion settings. Lastly, the 2-place connective ∧ ∨, was named platypus in [53], and features some properties of classical conjunction mingled with classical disjunction. Its multipleconclusion logic is characterized by the following two (familiar) rules.…”

Section: Illustrationsmentioning

confidence: 99%

Modular Many-Valued Semantics for Combined Logics

Caleiro¹,

Marcelino²

2023

J. symb. log.

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We obtain, for the first time, a modular many-valued semantics for combined logics, which is built directly from many-valued semantics for the logics being combined, by means of suitable universal operations over partial non-deterministic logical matrices. Our constructions preserve finite-valuedness in the context of multiple-conclusion logics, whereas, unsurprisingly, it may be lost in the context of single-conclusion logics. Besides illustrating our constructions over a wide range of examples, we also develop concrete applications of our semantic characterizations, namely regarding the semantics of strengthening a given many-valued logic with additional axioms, the study of conditions under which a given logic may be seen as a combination of simpler syntactically defined fragments whose calculi can be obtained independently and put together to form a calculus for the whole logic, and also general conditions for decidability to be preserved by the combination mechanism.

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Section: Illustrationsmentioning

confidence: 99%

Modular Many-Valued Semantics for Combined Logics

Caleiro¹,

Marcelino²

2023

J. symb. log.

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“…• Vor Aranda Utrero, Spanish Prize of Logic (Spain), "Completeness: from Husserl to Carnap" [25]. • Sérgio Marcelino, Amilcar Sernadas Logic Prize (Portugal), "An unexpected Boolean connective" [18]. In the following above map (Fig.…”

Section: Organization Of the 2nd World Logic Prizes Contestmentioning

confidence: 99%

The 2nd World Logic Prizes Contest, 7th UNILOG, Crete 2022

Béziau¹

2022

Log. Univers.

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We discuss the evolution of the World Logic Prizes Contest. In a first section, we describe how this contest developed, on the on hand by the creation of the Universal Logic Prize starting in 2005 at the 1st World Congress and School on Universal Logic in Montreux, Switzerland, on the other hand by the creation of the Newton da Costa Logic Prize in Brazil in 2014. These two projects joined in 2018 by the organization of the 1st World Logic Prizes Contest at the 6th World Congress and School on Universal Logic in Vichy, France. In a second section, we talk about the organization of the 2nd World Logic Prizes Contest to take place in April 2022 at the 6th World Congress and School on Universal Logic in Crete, Greece. We explain that there will be 15 contestants from 15 different countries with a good geographic distribution. In a third section, we discuss how this project can develop in the future with the creation of more logic prizes, the creation of similar prizes in other fields and the organization of a World Scientific Prizes Contest.

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“…In the above example, Boolean partial non-deterministic matrices were enough to illustrate both the effects of partiality and non-determinism, and the problems we shall investigate. A more in-depth analysis of logics defined by Boolean partial non-deterministic matrices can be found in [20]. We should emphasize, though, that the full power of partiality and non-determinism is better appreciated when considering PNmatrices with more than two truth-values, for which we refer the reader to the literature, notwithstanding the few examples we shall present later in the paper.…”

Section: Example 3 Let M Be a Pnmatrix If M Contains A Single Truth-value Then Eithermentioning

confidence: 99%

Computational Properties of Partial Non-deterministic Matrices and Their Logics

Marcelino

Caleiro

Filipe

2021

Logical Foundations of Computer Science

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Incorporating non-determinism and partiality in the traditional notion of logical matrix semantics has proven to be decisive in a myriad of recent compositionality results in logic. However, several important properties which are known to be computable for finite matrices have not been studied in this wider context of partial nondeterministic matrices (PNmatrices).This paper is dedicated to understanding how this generalization of the considered semantical structures affects the computational properties of basic problems regarding their induced logics, in particular their sets of theorems.We will show that the landscape is quite rich, as some problems keep their computational status, for others the complexity increases, and for a few decidability is lost. Namely, we show that checking if the logics defined by two finite PNmatrices have the same theorems is undecidable. This latter result is obtained by reduction from the undecidable problem of checking universality of term-DAG-automata.

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An Unexpected Boolean Connective

Cited by 5 publications

References 28 publications

Modular Many-Valued Semantics for Combined Logics

Modular Many-Valued Semantics for Combined Logics

The 2nd World Logic Prizes Contest, 7th UNILOG, Crete 2022

Computational Properties of Partial Non-deterministic Matrices and Their Logics

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