SEQUENT SYSTEMS FOR MODAL LOGICS
... are referred to [Gabbay, 1996], [Goré, 1999] and [Pliuškeviene, 1998]. Also Orlowska’s [1988; 1996] Rasiowa-Sikorski-style relational proof systems for normal modal logics will not be considered in the present chapter. In relational proof systems the logical object language is associated with a la ...
... are referred to [Gabbay, 1996], [Goré, 1999] and [Pliuškeviene, 1998]. Also Orlowska’s [1988; 1996] Rasiowa-Sikorski-style relational proof systems for normal modal logics will not be considered in the present chapter. In relational proof systems the logical object language is associated with a la ...
Harmony, Normality and Stability
... deductions in such a way that these ‘detours’ are avoided. Applying the reduction procedures should always turn deductions into new deductions. Trivial as this observation may sound, it shows that the point of having harmonious rules is not that they exhibit some feature independently of any logic i ...
... deductions in such a way that these ‘detours’ are avoided. Applying the reduction procedures should always turn deductions into new deductions. Trivial as this observation may sound, it shows that the point of having harmonious rules is not that they exhibit some feature independently of any logic i ...
thèse - IRIT
... logic provides a logical foundation for ASP: it captures the answer set semantics of logic programs and extends the syntax of answer set programs to more general propositional theories, i.e., finite sets of propositional formulas. This dissertation addresses modal logics underlying equilibrium logic ...
... logic provides a logical foundation for ASP: it captures the answer set semantics of logic programs and extends the syntax of answer set programs to more general propositional theories, i.e., finite sets of propositional formulas. This dissertation addresses modal logics underlying equilibrium logic ...
Foundations for Knowledge
... the situation calculus called ES (Lakemeyer & Levesque 2004). It does not use situation terms in the language and hence can directly serve as the language for tests. In fact, the tests in the above example are formulas in ES. Moreover, ES has a built-in notion of “this is all I know” adapted from Le ...
... the situation calculus called ES (Lakemeyer & Levesque 2004). It does not use situation terms in the language and hence can directly serve as the language for tests. In fact, the tests in the above example are formulas in ES. Moreover, ES has a built-in notion of “this is all I know” adapted from Le ...
A KE Tableau for a Logic of Formal Inconsistency - IME-USP
... pair T X and F X in DS. Second, all mCi KE rules with one or more premises (except (F ◦ ¬ n ◦) rules) preserve valuations. Note that (F ◦ ¬ n ◦) rules are taken into account by the last clause in Definition 2. That is, if we have a set of signed formulas that contains F ◦ ¬n ◦ X, every downward satu ...
... pair T X and F X in DS. Second, all mCi KE rules with one or more premises (except (F ◦ ¬ n ◦) rules) preserve valuations. Note that (F ◦ ¬ n ◦) rules are taken into account by the last clause in Definition 2. That is, if we have a set of signed formulas that contains F ◦ ¬n ◦ X, every downward satu ...
logic, programming and prolog (2ed)
... conventional programming languages is the declarative nature of logic. A program written in, for instance, Fortran can, in general, not be understood without taking operational considerations into account. That is, a Fortran program cannot be understood without knowing how it is going to be executed ...
... conventional programming languages is the declarative nature of logic. A program written in, for instance, Fortran can, in general, not be understood without taking operational considerations into account. That is, a Fortran program cannot be understood without knowing how it is going to be executed ...
logic for the mathematical
... not true; but the conclusion does not follow from them anyway. Actually, in that argument, the word “should” is probably better left out. Mostly, we want to deal with statements which simply state some kind of claimed fact, statements which are clearly either true or false, though which of the two m ...
... not true; but the conclusion does not follow from them anyway. Actually, in that argument, the word “should” is probably better left out. Mostly, we want to deal with statements which simply state some kind of claimed fact, statements which are clearly either true or false, though which of the two m ...
Combinaison des logiques temporelle et déontique pour la
... a resource for a certain period, the obligation to release a resource before a deadline, or the prohibition to execute a task for a too long period. Temporal and deontic logics seem well suited to specify such concepts. In this thesis, we study how to combine these logics. Firstly, we study the prod ...
... a resource for a certain period, the obligation to release a resource before a deadline, or the prohibition to execute a task for a too long period. Temporal and deontic logics seem well suited to specify such concepts. In this thesis, we study how to combine these logics. Firstly, we study the prod ...
MATH20302 Propositional Logic
... such as p, q, respectively s, t, not just for individual propositional variables, respectively propositional terms, but also as variables ranging over propositional variables, resp. propositional terms, (as we did just above). The definition above is an inductive one, with (0) being the base case an ...
... such as p, q, respectively s, t, not just for individual propositional variables, respectively propositional terms, but also as variables ranging over propositional variables, resp. propositional terms, (as we did just above). The definition above is an inductive one, with (0) being the base case an ...
Classical Propositional Logic
... A Henkin-style Completeness Proof for Natural Deduction Computability ...
... A Henkin-style Completeness Proof for Natural Deduction Computability ...
Formale Methoden der Softwaretechnik Formal methods of software
... The problem with this proof is step 8. In this step we have used step 3, a step that occurs within an earlier subproof. But it turns out that this sort of justification—one that reaches back inside a subproof that has already ended—is not legitimate. To understand why it’s not legitimate, we need to ...
... The problem with this proof is step 8. In this step we have used step 3, a step that occurs within an earlier subproof. But it turns out that this sort of justification—one that reaches back inside a subproof that has already ended—is not legitimate. To understand why it’s not legitimate, we need to ...
A Pebble Weighted Automata and Weighted Logics
... automata and word transducers appear as instances of that framework, which found its way into numerous application areas such as natural language processing and speech recognition or digital image compression (see [Droste et al. 2009, Part IV]). A logical characterization of weighted automata, howev ...
... automata and word transducers appear as instances of that framework, which found its way into numerous application areas such as natural language processing and speech recognition or digital image compression (see [Droste et al. 2009, Part IV]). A logical characterization of weighted automata, howev ...
Everything Else Being Equal: A Modal Logic for Ceteris Paribus
... of the notions we develop later, but also as a foundational standard against which we can evaluate our own results. In Section 3, we present a basic modal logic of weak and strict preference interpreted in ordered models of possible worlds, we discuss its expressive power and we provide a complete a ...
... of the notions we develop later, but also as a foundational standard against which we can evaluate our own results. In Section 3, we present a basic modal logic of weak and strict preference interpreted in ordered models of possible worlds, we discuss its expressive power and we provide a complete a ...
Ground Nonmonotonic Modal Logics - Dipartimento di Informatica e
... Recently, there have been a number of attempts to reconcile fix-point and semantic characterizations of modal nonmonotonic logics. In particular, Schwarz [30] proposed a semantics for McDermott and Doyle’s logics. However, the notion of minimal knowledge underlying the above cited works is stronger ...
... Recently, there have been a number of attempts to reconcile fix-point and semantic characterizations of modal nonmonotonic logics. In particular, Schwarz [30] proposed a semantics for McDermott and Doyle’s logics. However, the notion of minimal knowledge underlying the above cited works is stronger ...
Notes on the Science of Logic
... however, if you wish to stay with some other system. The same remark goes for notation. You need to learn to read ours, but you do not have to learn to write it.2 We will begin by reviewing this material with extreme brevity. In addition to the absolutely standard items listed above, there are a ser ...
... however, if you wish to stay with some other system. The same remark goes for notation. You need to learn to read ours, but you do not have to learn to write it.2 We will begin by reviewing this material with extreme brevity. In addition to the absolutely standard items listed above, there are a ser ...
The Journal of Functional and Logic Programming The MIT Press
... to L, that is, for every c ∈ L, either T |= ∃ The number of instances of CLP(X ) has grown so much in the last years that it would be impractical to cite them all. Classical CLP(X ) systems, so to speak, are CLP(R) [JMSY92], which computes over the constraint domain of linear arithmetic over the rea ...
... to L, that is, for every c ∈ L, either T |= ∃ The number of instances of CLP(X ) has grown so much in the last years that it would be impractical to cite them all. Classical CLP(X ) systems, so to speak, are CLP(R) [JMSY92], which computes over the constraint domain of linear arithmetic over the rea ...
Deductive Databases with Universally Quantified Conditions
... Such quantified literals are much more useful than the simpler ones discussed earlier. Usually, universally quantified statements are made on a subset of the universal domain. For example, someone may make an observation “ All men in this room are wearing a tie” rather than “All men are wearing a ti ...
... Such quantified literals are much more useful than the simpler ones discussed earlier. Usually, universally quantified statements are made on a subset of the universal domain. For example, someone may make an observation “ All men in this room are wearing a tie” rather than “All men are wearing a ti ...
1 Non-deterministic Phase Semantics and the Undecidability of
... — on the other hand, to position our approach w.r.t. the alternate undecidability result of [Brotherston and Kanovich 2010], we wish that this enriched version includes the models of (propositional) separation logic. We claim that the encoding of [Brotherston and Kanovich 2010] can be understood as ...
... — on the other hand, to position our approach w.r.t. the alternate undecidability result of [Brotherston and Kanovich 2010], we wish that this enriched version includes the models of (propositional) separation logic. We claim that the encoding of [Brotherston and Kanovich 2010] can be understood as ...
Conditional XPath
... relations. This is easily shown using a translation based on the equivalences in Table 1 (cf. also [28]). Arguably, the left and right axis relations must be available in an XPath dialect which calls itself navigational. For instance we need them to express XPath’s child::A[n] for n a natural number ...
... relations. This is easily shown using a translation based on the equivalences in Table 1 (cf. also [28]). Arguably, the left and right axis relations must be available in an XPath dialect which calls itself navigational. For instance we need them to express XPath’s child::A[n] for n a natural number ...
abdullah_thesis_slides.pdf
... Given d,t ∈ N, we can define the concept of type signatures of radius d with threshold t such that the values (#Type1 ,...,#Typen ) are counted only upto a threshold t and anything ≥ t is considered ∞. Two structures A and B, are said to be d-equivalent with threshold t if their type signatures with ...
... Given d,t ∈ N, we can define the concept of type signatures of radius d with threshold t such that the values (#Type1 ,...,#Typen ) are counted only upto a threshold t and anything ≥ t is considered ∞. Two structures A and B, are said to be d-equivalent with threshold t if their type signatures with ...
Intuitionistic and Modal Logic
... • Only partially successful. Not accepted by mathematicians in practice. • But study of intuitionistic proofs and formal systems very alive. Only by fully accepting intuitionistic methods does one get proofs that guarantees to exhibit objects that are proved to exist. One gets this way the construct ...
... • Only partially successful. Not accepted by mathematicians in practice. • But study of intuitionistic proofs and formal systems very alive. Only by fully accepting intuitionistic methods does one get proofs that guarantees to exhibit objects that are proved to exist. One gets this way the construct ...
Notes on Mathematical Logic David W. Kueker
... simpler context. The outline remains the same, and we will use some of the same ideas and techniques–especially the interplay of definition by recursion and proof by induction–when we come to first-order languages. This simpler formal language is called sentential logic. In this system, we ignore th ...
... simpler context. The outline remains the same, and we will use some of the same ideas and techniques–especially the interplay of definition by recursion and proof by induction–when we come to first-order languages. This simpler formal language is called sentential logic. In this system, we ignore th ...
relevance logic - Consequently.org
... and to a lesser extent on [Meyer, 1966], both of which are very much recommended to the reader for their wise heresy from logical tradition. Thus logical tradition (think of [Quine, 1953]) makes much of the grammatical distinction between ‘if, then’ (a connective), and ‘implies’ or its rough synonym ...
... and to a lesser extent on [Meyer, 1966], both of which are very much recommended to the reader for their wise heresy from logical tradition. Thus logical tradition (think of [Quine, 1953]) makes much of the grammatical distinction between ‘if, then’ (a connective), and ‘implies’ or its rough synonym ...
Relevant and Substructural Logics
... made clear in this area: the splitting of notions identified in stronger logical systems. Had Orlov noticed that one could define conjunction explicitly following the lattice definitions (as is done in intuitionistic logic, where the definitions in terms of negation and implication also fail) then h ...
... made clear in this area: the splitting of notions identified in stronger logical systems. Had Orlov noticed that one could define conjunction explicitly following the lattice definitions (as is done in intuitionistic logic, where the definitions in terms of negation and implication also fail) then h ...