First Order Smtl Logic and Quasi-witnessed Models
نویسندگان
چکیده
In this paper we prove strong completeness of axiomatic extensions of First Order SMTL logic adding the so-called quasi-witnessed axioms with respect to quasi-witnessed Models. In order to achieve this result, we make use of methods that are typical of Classical Predicate Logic, and have been later generalized by P. Hájek to cope with Predicate Fuzzy Logic. At the end of the paper, we obtain, as a particular case, the result of strong completeness, already proven by M.C. Laskowski and S. Malekpour, for Product Predicate Logic with respect to quasi-witnessed Models.
منابع مشابه
Strict core fuzzy logics and quasi-witnessed models
In this paper we prove strong completeness of axiomatic extensions of first-order strict core fuzzy logics with the so-called quasi-witnessed axioms with respect to quasi-witnessed models. As a consequence we obtain strong completeness of Product Predicate Logic with respect to quasi-witnessed models, already proven by M.C. Laskowski and S. Malekpour in [19]. Finally we study similar problems f...
متن کاملBeyond first order logic: From number of structures to structure of numbers: Part II
We study the history and recent developments in nonelementarymodel theory focusing on the framework of abstractelementary classes. We discuss the role of syntax and semanticsand the motivation to generalize first order model theory to nonelementaryframeworks and illuminate the study with concrete examplesof classes of models. This second part continues to study the question of catecoricitytrans...
متن کاملUsing Metric Temporal Logic to Specify Scheduling Problems
We introduce Scheduling MTL (SMTL) an extension of Metric Temporal Logic that supports the specification of complex scheduling problems with repeated and conditional occurrences of activities, and rich temporal relationships among them. We define the syntax and semantics of SMTL, and explore natural restrictions of the language to gain tractability. We also provide an algorithm for finding a sc...
متن کاملComputational complexities of axiomatic extensions of monoidal t-norm based logic
We study the computational complexity of some axiomatic extensions of the monoidal t-Norm based logic (MTL), namely NM corresponding to the logic of the so-called nilpotent minimum t-norm (due to Fodor [8]); and SMTL corresponding to left-continuous strict t-norms, introduced by Esteva (and others) in [4] and [5]. In particular, we show that the sets of 1-satisfiable and positively satisfiable ...
متن کاملDecidability of a Description Logic over Infinite-Valued Product Logic
This paper proves that validity and satisfiability of assertions in the Fuzzy Description Logic based on infinite-valued Product Logic with universal and existential quantifiers (which are non-interdefinable) is decidable when we only consider quasi-witnessed interpretations. We prove that this restriction is neither necessary for the validity problem (i.e., the validity of assertions in the Fu...
متن کامل