By Mauricio Osorio, José Luis Carballido, Claudia Zepeda (auth.), Félix Castro, Alexander Gelbukh, Miguel González (eds.)

The two-volume set LNAI 8265 and LNAI 8266 constitutes the court cases of the twelfth Mexican foreign convention on synthetic Intelligence, MICAI 2013, held in Mexico urban, Mexico, in November 2013. the complete of eighty five papers offered in those complaints have been rigorously reviewed and chosen from 284 submissions. the 1st quantity offers with advances in man made intelligence and its functions and is based within the following 5 sections: good judgment and reasoning; knowledge-based structures and multi-agent structures; common language processing; computer translation; and bioinformatics and scientific functions. the second one quantity offers with advances in smooth computing and its purposes and is dependent within the following 8 sections: evolutionary and nature-inspired metaheuristic algorithms; neural networks and hybrid clever platforms; fuzzy structures; computing device studying and development popularity; information mining; machine imaginative and prescient and photograph processing; robotics, making plans and scheduling and emotion detection, sentiment research and opinion mining.

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Con is a ﬁnite non-empty set of connectives; 3. arity is a mapping from Con to the set of non-negative integers, called the arity mapping; 4. val is a function from Con to the set of functions on V , called the valuation function, such that the arity of val (c) is arity(c), for all c ∈ Con. If arity(c) = m, then we call c an m-ary connective. The logic L is called a k-valued logic if k is the number of elements in V . For the rest of this paper we assume an arbitrary, but ﬁxed k-valued logic L = (V , Con, arity, val ).

We only consider many-valued logics with a ﬁnite set of truth values. Deﬁnition 1. A ﬁnite many-valued logic L is a triple (V , Con, arity, val ) where 1. V is a ﬁnite non-empty set of truth values; 2. Con is a ﬁnite non-empty set of connectives; 3. arity is a mapping from Con to the set of non-negative integers, called the arity mapping; 4. val is a function from Con to the set of functions on V , called the valuation function, such that the arity of val (c) is arity(c), for all c ∈ Con. If arity(c) = m, then we call c an m-ary connective.

Ak such that each Ai is a signed subformula of a signed formula in γ. Introduction rules These are all rules of Gγ are all rules of the form (2) restricted to signed subformulas of γ. Fig. 1. The sequent calculus Gγ Theorem 18. Let Π be a derivation of a sequent S. Then all signed formulas occurring in Π are signed subformulas of signed formulas in S. Proof. Straightforward by induction on the depth of Π. 5 The Inverse Method The inverse method tries to construct derivations from axioms to the goal, using the subformula property.